Tidal force

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Tidal_force 

Figure 1: Tidal interaction between the spiral galaxy NGC 169 and a smaller companion

The tidal force or tide-generating force is the difference in gravitational attraction between different points in a gravitational field, causing bodies to be pulled unevenly and as a result are being stretched towards the attraction. It is the differential force of gravity, the net between gravitational forces, the derivative of gravitational potential, the gradient of gravitational fields. Therefore tidal forces are a residual force, a secondary effect of gravity, highlighting its spatial elements, making the closer near-side more attracted than the more distant far-side.

This produces a range of tidal phenomena, such as ocean tides. Earth's tides are mainly produced by the relative close gravitational field of the Moon and to a lesser extent by the stronger, but further away gravitational field of the Sun. The ocean on the side of Earth facing the Moon is being pulled by the gravity of the Moon away from Earth's crust, while on the other side of Earth there the crust is being pulled away from the ocean, resulting in Earth being stretched, bulging on both sides, and having opposite high-tides. Tidal forces viewed from Earth, that is from a rotating reference frame, appear as centripetal and centrifugal forces, but are not caused by the rotation.

Further tidal phenomena include solid-earth tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. Tidal forces have also been shown to be fundamentally related to gravitational waves.

In celestial mechanics, the expression tidal force can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Earth), but is also perturbed by the gravitational effects of a third body (for example, the Moon). The perturbing force is sometimes in such cases called a tidal force (for example, the perturbing force on the Moon): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.

Explanation

Figure 2: Shown in red, the Moon's gravity residual field at the surface of the Earth is known (along with another and weaker differential effect due to the Sun) as the tide generating force. This is the primary mechanism driving tidal action, explaining two simultaneous tidal bulges. Earth's rotation accounts further for the occurrence of two high tides per day on the same location. In this figure, the Earth is the central black circle while the Moon is far off to the right. It shows both the tidal field (thick red arrows) and the gravity field (thin blue arrows) exerted on Earth's surface and center (label O) by the Moon (label S). The outward direction of the arrows on the right and left of the Earth indicates that where the Moon is at zenith or at nadir.

When a body (body 1) is acted on by the gravity of another body (body 2), the field can vary significantly on body 1 between the side of the body facing body 2 and the side facing away from body 2. Figure 2 shows the differential force of gravity on a spherical body (body 1) exerted by another body (body 2).

These tidal forces cause strains on both bodies and may distort them or even, in extreme cases, break one or the other apart. The Roche limit is the distance from a planet at which tidal effects would cause an object to disintegrate because the differential force of gravity from the planet overcomes the attraction of the parts of the object for one another. These strains would not occur if the gravitational field were uniform, because a uniform field only causes the entire body to accelerate together in the same direction and at the same rate.

Size and distance

The relationship of an astronomical body's size, to its distance from another body, strongly influences the magnitude of tidal force. The tidal force acting on an astronomical body, such as the Earth, is directly proportional to the diameter of the Earth and inversely proportional to the cube of the distance from another body producing a gravitational attraction, such as the Moon or the Sun. Tidal action on bath tubs, swimming pools, lakes, and other small bodies of water is negligible.

Figure 3: Graph showing how gravitational attraction drops off with increasing distance from a body

Figure 3 is a graph showing how gravitational force declines with distance. In this graph, the attractive force decreases in proportion to the square of the distance (Y = 1/X²), while the slope (Y′ = −2/X³) is inversely proportional to the cube of the distance.

The tidal force corresponds to the difference in Y between two points on the graph, with one point on the near side of the body, and the other point on the far side. The tidal force becomes larger, when the two points are either farther apart, or when they are more to the left on the graph, meaning closer to the attracting body.

For example, even though the Sun has a stronger overall gravitational pull on Earth, the Moon creates a larger tidal bulge because the Moon is closer. This difference is due to the way gravity weakens with distance: the Moon's closer proximity creates a steeper decline in its gravitational pull as you move across Earth (compared to the Sun's very gradual decline from its vast distance). This steeper gradient in the Moon's pull results in a larger difference in force between the near and far sides of Earth, which is what creates the bigger tidal bulge.

Gravitational attraction is inversely proportional to the square of the distance from the source. The attraction will be stronger on the side of a body facing the source, and weaker on the side away from the source. The tidal force is proportional to the difference.

Sun, Earth, and Moon

The Sun is about 20 million times the Moon's mass, and acts on the Earth over a distance about 400 times larger than that of the Moon. Because of the cubic dependence on distance, this results in the solar tidal force on the Earth being about half that of the lunar tidal force.

Gravitational body causing tidal force		Body subjected to tidal force			Tidal acceleration
Body	Mass (${\displaystyle m}$)	Body	Radius (${\displaystyle r}$)	Distance (${\displaystyle d}$)	${\displaystyle Gm\frac{2r}{d^3}}$
Sun	1.99×1030 kg	Earth	6.37×106 m	1.50×1011 m	5.05×10−7 m⋅s−2
Moon	7.34×1022 kg	Earth	6.37×106 m	3.84×108 m	1.10×10−6 m⋅s−2
Earth	5.97×1024 kg	Moon	1.74×106 m	3.84×108 m	2.44×10−5 m⋅s−2
G is the gravitational constant = 6.674×10−11 m3⋅kg−1⋅s−2

Effects

Figure 4: Saturn's rings are inside the orbits of its principal moons. Tidal forces oppose gravitational coalescence of the material in the rings to form moons.

In the case of an infinitesimally small elastic sphere, the effect of a tidal force is to distort the shape of the body without any change in volume. The sphere becomes an ellipsoid with two bulges, pointing towards and away from the other body. Larger objects distort into an ovoid, and are slightly compressed, which is what happens to the Earth's oceans under the action of the Moon. All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon.

When a body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotational kinetic energy as heat. In the case for the Earth, and Earth's Moon, the loss of rotational kinetic energy results in a gain of about 2 milliseconds per century. If the body is close enough to its primary, this can result in a rotation which is tidally locked to the orbital motion, as in the case of the Earth's moon. Tidal heating produces dramatic volcanic effects on Jupiter's moon Io. Stresses caused by tidal forces also cause a regular monthly pattern of moonquakes on Earth's Moon.

Tidal forces contribute to ocean currents, which moderate global temperatures by transporting heat energy toward the poles. It has been suggested that variations in tidal forces correlate with cool periods in the global temperature record at 6- to 10-year intervals, and that harmonic beat variations in tidal forcing may contribute to millennial climate changes. No strong link to millennial climate changes has been found to date.

Figure 5: Comet Shoemaker-Levy 9 in 1994 after breaking up under the influence of Jupiter's tidal forces during a previous pass in 1992.

Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes, where they are responsible for the "spaghettification" of infalling matter. Tidal forces create the oceanic tide of Earth's oceans, where the attracting bodies are the Moon and, to a lesser extent, the Sun. Tidal forces are also responsible for tidal locking, tidal acceleration, and tidal heating. Tides may also induce seismicity.

By generating conducting fluids within the interior of the Earth, tidal forces also affect the Earth's magnetic field.

Formulation

Figure 7: Tidal force is responsible for the merge of galactic pair MRK 1034.

Figure 8: Graphic of tidal forces. The top picture shows the gravity field of a body to the right (not shown); the lower shows their residual gravity once the field at the centre of the sphere is subtracted; this is the tidal force. For visualization purposes, the top arrows may be assumed as equal to 1 N, 2 N, and 3 N (from left to right); the resulting bottom arrows would equal, respectively, −1 N (negative, thus 180-degree rotated), 0 N (invisible), and 1 N. See Figure 2 for a more detailed version

For a given (externally generated) gravitational field, the tidal acceleration at a point with respect to a body is obtained by vector subtraction of the gravitational acceleration at the center of the body (due to the given externally generated field) from the gravitational acceleration (due to the same field) at the given point. Correspondingly, the term tidal force is used to describe the forces due to tidal acceleration. Note that for these purposes the only gravitational field considered is the external one; the gravitational field of the body (as shown in the graphic) is not relevant. (In other words, the comparison is with the conditions at the given point as they would be if there were no externally generated field acting unequally at the given point and at the center of the reference body. The externally generated field is usually that produced by a perturbing third body, often the Sun or the Moon in the frequent example-cases of points on or above the Earth's surface in a geocentric reference frame.)

Tidal acceleration does not require rotation or orbiting bodies; for example, the body may be freefalling in a straight line under the influence of a gravitational field while still being influenced by (changing) tidal acceleration.

By Newton's law of universal gravitation and laws of motion, a body of mass m at distance R from the center of a sphere of mass M feels a force ${\overrightarrow{F}}_g$,

$${\displaystyle {\overrightarrow{F}}_g=-\hat{r}G\frac{Mm}{R^2}}$$

equivalent to an acceleration ${\overrightarrow{a}}_g$,

$${\displaystyle {\overrightarrow{a}}_g=-\hat{r}G\frac{M}{R^2}}$$

where $\hat{r}$ is a unit vector pointing from the body M to the body m (here, acceleration from m towards M has negative sign).

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆r be the (relatively small) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆r, then the new particle considered may be located on its surface, at a distance (R ± ∆r) from the centre of the sphere of mass M, and ∆r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of m's own mass, we have the acceleration on the particle due to gravitational force towards M as:

$${\displaystyle {\overrightarrow{a}}_g=-\hat{r}G\frac{M}{(R\pm \mathrm{\Delta }r{)}^2}}$$

Pulling out the R² term from the denominator gives:

$${\displaystyle {\overrightarrow{a}}_g=-\hat{r}G\frac{M}{R^2}\frac{1}{{\left(1\pm \frac{\mathrm{\Delta }r}{R}\right)}^2}}$$

The Maclaurin series of $1/(1\pm x{)}^2$ is $1\mp 2x+3x^2\mp \cdots$ which gives a series expansion of:

$${\displaystyle {\overrightarrow{a}}_g=-\hat{r}G\frac{M}{R^2}\pm \hat{r}G\frac{2M}{R^2}\frac{\mathrm{\Delta }r}{R}+\cdots }$$

The first term is the gravitational acceleration due to M at the center of the reference body $m$, i.e., at the point where $\mathrm{\Delta }r$ is zero. This term does not affect the observed acceleration of particles on the surface of m because with respect to M, m (and everything on its surface) is in free fall. When the force on the far particle is subtracted from the force on the near particle, this first term cancels, as do all other even-order terms. The remaining (residual) terms represent the difference mentioned above and are tidal force (acceleration) terms. When ∆r is small compared to R, the terms after the first residual term are very small and can be neglected, giving the approximate tidal acceleration ${\overrightarrow{a}}_{t,\text{axial}}$ for the distances ∆r considered, along the axis joining the centers of m and M:

$${\displaystyle {\overrightarrow{a}}_{t,\text{axial}}\approx \pm \hat{r}2\mathrm{\Delta }rG\frac{M}{R^3}}$$

When calculated in this way for the case where ∆r is a distance along the axis joining the centers of m and M, ${\overrightarrow{a}}_t$ is directed outwards from to the center of m (where ∆r is zero).

Tidal accelerations can also be calculated away from the axis connecting the bodies m and M, requiring a vector calculation. In the plane perpendicular to that axis, the tidal acceleration is directed inwards (towards the center where ∆r is zero), and its magnitude is $\frac{1}{2}\left|{\overrightarrow{a}}_{t,\text{axial}}\right|$ in linear approximation as in Figure 2.

The tidal accelerations at the surfaces of planets in the Solar System are generally very small. For example, the lunar tidal acceleration at the Earth's surface along the Moon–Earth axis is about 1.1×10⁻⁷ g, while the solar tidal acceleration at the Earth's surface along the Sun–Earth axis is about 0.52×10⁻⁷ g, where g is the gravitational acceleration at the Earth's surface. Hence the tide-raising force (acceleration) due to the Sun is about 45% of that due to the Moon. The solar tidal acceleration at the Earth's surface was first given by Newton in the Principia.

Risk

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Risk 

Firefighters are exposed to risks of fire and building collapse during their work.

Risk is the possibility of something bad happening, comprising a level of uncertainty about the effects and implications of an activity, particularly negative and undesirable consequences.

Harbor sign warning visitors that use of the walkway is "at your own risk"

Risk theory, assessment, and management are applied but substantially differ in different practice areas, such as business, economics, environment, finance, information technology, health, insurance, safety, security, and privacy. The international standard for risk management, ISO 31000, provides general guidelines and principles on managing risks faced by organizations.

Artist's impression of a major asteroid impact, an example of a global catastrophic risk.

Definition

The Oxford English Dictionary (OED) cites the earliest use of the word in English (in the spelling of risque from its French original, 'risque') as of 1621, and the spelling as risk from 1655. While including several other definitions, the OED 3rd edition defines risk as "(Exposure to) the possibility of loss, injury, or other adverse or unwelcome circumstance; a chance or situation involving such a possibility". The Cambridge Advanced Learner's Dictionary defines risk as "the possibility of something bad happening". Some have argued that the definition of risk is subjective and context-specific. The International Organization for Standardization (ISO) 31073 defines risk as:

effect of uncertainty on objectives

Note 1: An effect is a deviation from the expected. It can be positive, negative or both, and can address, create or result in opportunities and threats.

Note 2: Objectives can have different aspects and categories, and can be applied at different levels.

Note 3: Risk is usually expressed in terms of risk sources, potential events, their consequences and their likelihood.

Other general definitions include:

• "Source of harm". The earliest use of the word "risk" was as a synonym for the much older word "hazard", meaning a potential source of harm. This definition comes from Blount's "Glossographia" (1661) and was the main definition in the OED 1st (1914) and 2nd (1989) editions. Modern equivalents refer to "unwanted events" or "something bad that might happen".
• "Chance of harm". This definition comes from Johnson's "Dictionary of the English Language" (1755), and has been widely paraphrased, including "possibility of loss" or "probability of unwanted events".
• "Uncertain events affecting objectives". This definition was adopted by the Association for Project Management (1997). With slight rewording it became the definition in ISO Guide 73.
• "Uncertainty of outcome". This definition was adopted by the UK Cabinet Office (2002) to encourage innovation to improve public services. It allowed "risk" to describe either "positive opportunity or negative threat of actions and events".
• "Potential returns from an event ['a thing that happens or takes place'], where the returns are any changes, effects, consequences, and so on, of the event". This definition from Newsome (2014) expands the neutrality of 'risk' akin to the UK Cabinet Office (2002) and Knight (1921).
• "Human interaction with uncertainty". This definition comes from Cline (2015) in the context of adventure education.

Versus uncertainty

In his seminal 1921 work Risk, Uncertainty, and Profit, Frank Knight established the distinction between risk and uncertainty.

... Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. The term "risk," as loosely used in everyday speech and in economic discussion, really covers two things which, functionally at least, in their causal relations to the phenomena of economic organization, are categorically different. ... The essential fact is that "risk" means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomenon depending on which of the two is really present and operating. ... It will appear that a measurable uncertainty, or "risk" proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We ... accordingly restrict the term "uncertainty" to cases of the non-quantitive type.

Thus, Knightian uncertainty is immeasurable, not possible to calculate, while in the Knightian sense risk is measurable.

By field

Definitions of risk

Field	Definition	Sources	Related concepts
Economics	Uncertainty about loss	Willett's "Economic Theory of Risk and Insurance" (1901).
Insurance	Measurable uncertainty	Knight's "Risk, Uncertainty and Profit" (1921).	Knightian uncertainty, mortality risk, longevity risk, interest rate risk
	Possibility of an event occurring which causes injury or loss	Lloyd's.
Finance	Volatility of return	Markovitz's "Portfolio Selection" (1952).	Financial risk management, Risk aversion
			Components: Downside risk, Upside risk, Inherent risk, Benefit risk
			Business risks: Enterprise risk management, Audit risk, Process risk, Legal risk, Reputational risk, Peren–Clement index
			Investments: Modern portfolio theory, Value at risk, Hedge
			Types of financial risks: Market risk, Credit risk, Liquidity risk, Operational risk
Decision theory	Statistically expected loss	Wald (1939). Used in planning of Delta Works in 1953. Adopted by the US Nuclear Regulatory Commission in 1975. Remains widely used.
Bayesian analysis	Scenarios, probabilities and consequences: Consequences and associated uncertainty; likelihood and severity of events	Kaplan & Garrick (1981). Found in ISO Guide 73 Note 4.
Occupational health and safety	Combination of the likelihood and consequence(s) of a specified hazardous event occurring	Occupational Health and Safety Assessment Series (OHSAS) standard OHSAS 18001, 1999.	Occupational hazard, High reliability organisation, Probabilistic risk assessment, WASH-1400
Cybersecurity	Asset, threat and vulnerability	Threat Analysis Group (2010).	Information security, IT risk management, IT risk
Environment	Chance of harmful effects to human health or to ecological systems	United States Environmental Protection Agency.	Environmental hazards, Environmental issues, Environmental protection
Health	Possibility that something will cause harm	Centres for Disease Control and Prevention.	Epidemiology, Risk factors, Health risk assessment, Relative risk, Mortality rate, Loss of life expectancy
Project management	An uncertain event or condition that, if it occurs, has a positive or negative effect on a project's objectives	Project Management Institute.	Project risk management
Security	Any event that could result in the compromise of organizational assets i.e. the unauthorized use, loss, damage, disclosure or modification of organizational assets for the profit, personal interest or political interests of individuals, groups or other entities		Security management

Mathematical

Triplets

Risk is often considered to be a set of triplets

${\displaystyle \text{R}=(s_i,p_i,x_i)}$ for i = 1,2,....,N

where:

${\displaystyle s_i}$ is a scenario describing a possible event

${\displaystyle p_i}$ is the probability of the scenario

${\displaystyle x_i}$ is the consequence of the scenario

${\displaystyle N}$ is the number of scenarios chosen to describe the risk

Risks expressed in this way can be shown in a risk register or a risk matrix. They may be quantitative or qualitative, and can include positive as well as negative consequences.

An updated version recommends the following general description of risk:

${\displaystyle R=(A,C,U,P,K)}$

where:

${\displaystyle A}$ is an event that might occur

${\displaystyle C}$ is the consequences of the event

${\displaystyle U}$ is an assessment of uncertainties

${\displaystyle P}$ is a knowledge-based probability of the event

${\displaystyle K}$ is the background knowledge that U and P are based on

Probability distributions

If all the consequences are expressed in the same units (or can be converted into a consistent loss function), the risk can be expressed as a probability density function describing the uncertainty about outcome:

${\displaystyle R=p(x)}$

This can also be expressed as a cumulative distribution function (CDF) (or S curve). One way of highlighting the tail of this distribution is by showing the probability of exceeding given losses, known as a complementary cumulative distribution function, plotted on logarithmic scales. For example, frequency-number diagrams show the annual frequency of exceeding given numbers of fatalities. Another way of summarizing the size of the distribution's tail is the loss with a certain probability of exceedance, that is, the value at risk.

Expected values

Risk is often measured as the expected value of the loss. This combines the probabilities and consequences into a single value. See also expected utility. The simplest case is a binary possibility of Accident or No accident. The associated formula for calculating risk is then:

${\displaystyle R=(\text{probability of the accident occurring})\times (\text{expected loss in case of the accident})}$

In a situation with several possible accident scenarios, total risk is the sum of the risks for each scenario, provided that the outcomes are comparable:

${\displaystyle R=\sum _{i=1}^N{p}_i{x}_i}$

In statistical decision theory, the risk function is defined as the expected value of a given loss function as a function of the decision rule used to make decisions in the face of uncertainty.

A disadvantage of defining risk as the product of impact and probability is that it presumes, unrealistically, that decision-makers are risk-neutral. A risk-neutral person's utility is proportional to the expected value of the payoff. For example, a risk-neutral person would consider 20% chance of winning $1 million exactly as desirable as getting a certain $200,000. However, most decision-makers are not actually risk-neutral and would not consider these equivalent choices. Pascal's mugging is a philosophical thought experiment that demonstrates issues in assessing risk solely by the expected value of loss or return.

Outcome frequencies

Risks of discrete events such as accidents are often measured as outcome frequencies, or expected rates of specific loss events per unit time. When small, frequencies are numerically similar to probabilities, but have dimensions of ⁠1/t⁠ and can sum to more than 1. Typical outcomes expressed this way include:

• Individual risk - the frequency of a given level of harm to an individual. It often refers to the expected annual probability of death, and is then comparable to the mortality rate.
• Group (or societal risk) – the relationship between the frequency and the number of people suffering harm.
• Frequencies of property damage or total loss.
• Frequencies of environmental damage such as oil spills.

Financial risk

In finance, volatility is the degree of variation of a trading price over time, usually measured by the standard deviation of logarithmic returns. Modern portfolio theory measures risk using the variance (or standard deviation) of asset prices. The risk is then:

${\displaystyle R=\sigma }$

The beta coefficient measures the volatility of an individual asset to overall market changes. This is the asset's contribution to systematic risk, which cannot be eliminated by portfolio diversification. It is the covariance between the asset's return r_i and the market return r_m, expressed as a fraction of the market variance:

${\displaystyle {\beta }_i=\frac{{\sigma }_{im}}{{\sigma }_m^2}=\frac{\mathrm{C}\mathrm{o}\mathrm{v}(r_i,r_m)}{\mathrm{V}\mathrm{a}\mathrm{r}(r_m)}}$

Risk-neutral measure

In mathematical finance, a risk-neutral measure is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under the measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing.

Let ${\displaystyle S}$ be a d-dimensional market representing the price processes of the risky assets, ${\displaystyle B}$ the risk-free bond and ${\displaystyle (\mathrm{\Omega },\mathcal{F},P)}$the underlying probability space. Then a measure ${\displaystyle Q}$ is a risk-neutral measure if

1. ${\displaystyle Q\approx P}$, i.e., ${\displaystyle Q}$ is equivalent to ${\displaystyle P}$,
2. the processes ${\displaystyle {\left(\frac{S_t^i}{B_t}\right)}_t}$ are (local) martingales w.r.t. ${\displaystyle Q}$ ${\displaystyle \mathrm{\forall }i=1,\dots ,d}$.

Mandelbrot's mild and wild theory

Benoit Mandelbrot distinguished between "mild" and "wild" risk and argued that risk assessment and analysis must be fundamentally different for the two types of risk. Mild risk follows normal or near-normal probability distributions, is subject to regression to the mean and the law of large numbers, and is therefore relatively predictable. Wild risk follows fat-tailed distributions, e.g., Pareto or power-law distributions, is subject to regression to the tail (infinite mean or variance, rendering the law of large numbers invalid or ineffective), and is therefore difficult or impossible to predict. A common error in risk assessment and analysis is to underestimate the wildness of risk, assuming risk to be mild when in fact it is wild, which must be avoided if risk assessment and analysis are to be valid and reliable, according to Mandelbrot.

Estimation

• Proxy or analogue data from other contexts, presumed to be similar in some aspects of risk.
• Theoretical models, such as Monte Carlo simulation and Quantitative risk assessment software.
• Logical models, such as Bayesian networks, fault tree analysis and event tree analysis
• Expert judgement, such as absolute probability judgement or the Delphi method.

Management

Risk management is the set of actions that organisations take to avoid and mitigate downside risks, taking into account factors such as the possibility of upside risk opportunities, innovation, the environment, safety, scientific evidence, culture, politics, and law. Risk management operates at the strategic, operational, and individual level, and may form part of an overarching governance, risk, and compliance strategy. It comprises the assessment of risk as regards an organisation's objectives and strategies, as well as risk mitigation options, such as risk transformation, risk transfer, risk avoidance, risk reduction, and risk retention.

Assessment

Risk assessment is a systematic approach to recognising and characterising risks, and evaluating their significance, in order to support decisions about how to manage them. ISO 31000 defines it in terms of its components as "the overall process of risk identification, risk analysis and risk evaluation":

• Risk identification is "the process of finding, recognizing and recording risks". It "involves the identification of risk sources, events, their causes and their potential consequences." ISO 31000 describes it as the first step in a risk assessment process, preceding risk analysis and risk evaluation. In safety contexts, where risk sources are known as hazards, this step is known as "hazard identification".
• The ISO defines risk analysis as "the process to comprehend the nature of risk and to determine the level of risk". In the ISO 31000 risk assessment process, risk analysis follows risk identification and precedes risk evaluation. Risk analysis often uses data on the probabilities and consequences of previous events.
• Risk evaluation involves comparing estimated levels of risk against risk criteria to determine the significance of the risk and make decisions about risk treatment actions. In most activities, risks can be reduced by adding further controls or other treatment options, but typically this increases cost or inconvenience. It is rarely possible to eliminate risks altogether without discontinuing the activity. Sometimes it is desirable to increase risks to secure valued benefits. Risk criteria are intended to guide decisions on these issues.

For example, the tolerability of risk framework, developed by the UK Health and Safety Executive, divides risks into three bands:

• Unacceptable risks – only permitted in exceptional circumstances.
• Tolerable risks – to be kept as low as reasonably practicable (ALARP), taking into account the costs and benefits of further risk reduction.
• Broadly acceptable risks – not normally requiring further reduction.

Attitude, appetite and tolerance

The terms risk appetite, attitude, and tolerance are often used similarly to describe an organisation's or individual's attitude towards risk-taking. One's attitude may be described as risk-averse, risk-neutral, or risk-seeking.

Mitigation

• Risk transformation describes the process of not only mitigating risks but also employing risk factors into advantages.
• Risk transfer is the shifting of risks from one party to another, typically an insurer.

Psychology of risk

Risk perception

Risk perception is the subjective judgement that people make about the characteristics and severity of a risk. At its most basic, the perception of risk is an intuitive form of risk analysis.

Adults have an intuitive understanding of risk, which may not be exclusive to humans. Many ancient societies believed in divinely determined fates, and attempts to influence the gods can be seen as early forms of risk management. Early uses of the word 'risk' coincided with an erosion of belief in divinely ordained fate. Notwithstanding, intuitive perceptions of risk are often inaccurate owing to reliance on psychological heuristics, which are subject to systematic cognitive biases. In particular, the accuracy of risk perception can be adversely affected by the affect heuristic, which relies on emotion to make decisions.

The availability heuristic is the process of judging the probability of an event by the ease with which instances come to mind. In general, rare but dramatic causes of death are over-estimated while common unspectacular causes are under-estimated; an "availability cascade" is a self-reinforcing cycle in which public concern about relatively minor events is amplified by media coverage until the issue becomes politically important. Despite the difficulty of thinking statistically, people are typically subject to the overconfidence effect in their judgements, tending to overestimate their understanding of the world and underestimate the role of chance, with even experts subject to this effect. Other biases that affect the perception of risk include ambiguity aversion.

Paul Slovic's "psychometric paradigm" assumes that risk is subjectively defined by individuals, influenced by factors such as lack of control, catastrophic potential, and severity of consequences, such that risk perception can be psychometrically measured by surveys. Slovic argues that intuitive emotional reactions are the predominant method by which humans evaluate risk, and that a purely statistical approach to disasters lacks emotion and thus fails to convey the true meaning of disasters and fails to motivate proper action to prevent them. This theory has received support from retrospective studies and evolutionary psychology. Hazards with high perceived risk are therefore, in general, seen as less acceptable and more in need of reduction.

Cultural theory of risk views risk perception as a collective phenomenon by which different cultures select some risks for attention and ignore others, with the aim of maintaining their particular way of life. Hence risk perception varies according to the preoccupations of the culture. The theory outlines two categories, the degree of binding to social groups, the degree of social regulation. Cultural theory can be used to explain why it can be difficult for people with different world-views to agree about whether a hazard is acceptable, and why risk assessments may be more persuasive for some people than others. However, there is little quantitative evidence that shows cultural biases are strongly predictive of risk perception.

Decision theory

Main articles: Decision theory and Prospect theory

In decision theory, regret (and anticipation of regret) can play a significant part in decision-making, distinct from risk aversion. Framing is also a fundamental problem with all forms of risk assessment. In particular, because of bounded rationality, the risk of extreme events is discounted because the probability is too low to evaluate intuitively. As an example, one of the leading causes of death is road accidents caused by drunk driving – partly because any given driver frames the problem by largely or totally ignoring the risk of a serious or fatal accident. The right prefrontal cortex has been shown to take a more global perspective, while greater left prefrontal activity relates to local or focal processing. Reference class forecasting is a forecasting method by which biases associated with risks can be mitigated.

Risk taking

Psychologists have run randomised experiments with a treatment and control group to ascertain the effect of different psychological factors that may be associated with risk taking, finding that positive and negative feedback about past risk taking can affect future risk taking. For example, one experiment showed that belief in competence correlated with risk-taking behavior. Risk compensation is a theory that suggests that people typically adjust their behavior in response to the perceived level of risk, becoming more careful where they sense greater risk and less careful if they feel more protected. People also show risk aversion, such that they reject fair risky offers because of the perception of loss. Further, intuitive responses have been found to be less risk-averse than subsequent reflective response.

Sex differences

Sex differences in financial decision making are relevant and significant. Numerous studies have found that women tend to be financially more risk-averse than men and hold safer portfolios. Scholarly research has documented systematic differences in financial decisions such as buying investments versus insurance, donating to ingroups versus outgroups (such as terrorism victims in Iraq versus the United States), spending in stores, and the endowment effect-or asking price for goods people have.

Philosophy of risk

Peter L. Bernstein (2012) showed that people used risk estimates before statistics and probability calculations were developed. Instead of relying on numbers, people used narratives and letters. Captains and merchants shared voyage stories at coffeehouses, comparing notes about hazards on new routes and seasonal patterns. Through a web of correspondents, letters became increasingly important as people could update their beliefs about weather, wars, or piracy over long distances. These qualitative data helped investors and underwriters judge how dicey a proposed voyage felt.

This kind of evidence has led philosophers to think there is more to (objective) risk than the likelihood of an undesirable outcome. Ebert et al. (2020) suggest distinguishing risk monists from risk pluralists: risk monists argue that there is just one correct way to understand risk. Tversky and Kahneman can be considered monists in this sense; probability judgments that diverged from the probability calculus were deemed wrong or biased. By contrast, pluralists claim that there are different, valid notions of risk. On this view, people who lived before statistics were developed may have been doing something legitimate when they estimated risks—even if those estimates conflict with a statistical notion. Without statistics, what else could they have done?

According to the modal account of risk, a situation is risky when nearby possible worlds—differing only slightly from the actual one—contain serious harm. Risk tracks the closeness of such bad outcomes rather than their probability; hence a low-chance disaster may still count as high risk if only a small change would have led to it. On the normic account of risk, a situation is risky when the bad outcome would be normal or unsurprising. Risk is assessed through system functions and norms rather than bare probability. A harm counts as high risk when it would occur in the most normal continuations of the present setup; the less departure from normality needed for the harm, the greater the risk. Especially in domains where we lack predictive power, such approaches allow us to consider risk without relying on unknown probabilities, as illustrated by the normic account of suicide risk.

Society and culture

Risk and autonomy

The experience of many people who rely on human services for support is that 'risk' is often used as a reason to prevent them from gaining further independence or fully accessing the community, and that these services are often unnecessarily risk averse. "People's autonomy used to be compromised by institution walls, now it's too often our risk management practices", according to John O'Brien. Michael Fischer and Ewan Ferlie (2013) find that contradictions between formal risk controls and the role of subjective factors in human services (such as the role of emotions and ideology) can undermine service values, so producing tensions and even intractable and 'heated' conflict.

Risk society

Main article: Risk society

Anthony Giddens and Ulrich Beck argued that whilst humans have always been subjected to a level of risk – such as natural disasters – these have usually been perceived as produced by non-human forces. Modern societies, however, are exposed to risks such as pollution, that are the result of the modernization process itself. Giddens defines these two types of risks as external risks and manufactured risks. The term Risk society was coined in the 1980s and its popularity during the 1990s was both as a consequence of its links to trends in thinking about wider modernity, and also to its links to popular discourse, in particular the growing environmental concerns during the period.