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### [New Corona] Kanagawa Prefecture, low-risk infected people are treated as "voluntary medical treatment" Pulse oximeter distribution, meal distribution ...

** ***If you write the contents roughly*

However, in reality, it must be said that it is not enough to avoid risks with this new response.** **

In Kanagawa Prefecture, on the 27th, the spread of infection by the new Coronaomicron strain has put pressure on health centers, testing centers, fever outpatients, etc ...** → Continue reading**

**MEDIAN TALKS**

To the Japanese medical community, which is facing the super-aging society and the tightness of medical resources at the same time, from each viewpoint, we will convey the voice of medical personnel striving to provide better medical care as it is, from a clinical perspective, a field perspective , This is a blog site for patients.

### Wikipedia related words

If there is no explanation, there is no corresponding item on Wikipedia.

# risk avoidance

**risk avoidance**(Risk Kaihi,British: risk risk) Is due to uncertainty about the futureriskTry to avoidEconomicsInPreferenceIs.Also called danger avoidance.Risk lovers as antonymsBritish: risk loving) And risk-neutral (British: risk neutral).Average dispersion type as described laterUtility functionAnd relative risk aversion Many utility functions used in economics, such as constant-type utility functions, express risk-averse preferences and are the nature of preferences used to describe decision-making under uncertainty. Is a common one.

## Definition

Random variable for profits from any gambling A age, Expected value Suppose there is.Further ensure gambling B Gambling that will give you the benefit of.At this time, there is a preference**Risk aversion**(British: risk averse) Means that gambling B is at least as good as or better than gambling A in its preference.^{[1]}.

Risk-loving is when gambling A is at least as good as or better than gambling B.Risk-neutral means when gambling A and gambling B are indiscriminate.

## Certainty equivalence

A preference relationshipExpected utilityfunction

It is represented by.However, Is some kind of function.This function Is a Bernoulli utility function (British: Bernoulli utility function）^{[2]}, Basic utility function (British: cardinal utility function）^{[3]}And so on.At this time, the random variable Function of about**Certainty equivalence**(British: certainty equivalent) Is a constant that satisfies the following Say that^{[4]}^{[5]}.

Certainty equivalence is an uncertain benefit Refers to the benefits paid for gambling without uncertainty that results in the same level of utility as gambling that results in.Bernoulli utility function When is monotonous and non-decreasing, the following three are known to be equivalent^{[6]}.

- The preference expressed by the expected utility function in equation (1) is risk aversion.

- When the preference is expressed by the expected utility function in formula (1), TheConcave function.

- Any random variable Function of Certainty equivalence about Then, Is established.

From the third condition, decision makers with risk-averse preferences are uncertain.gamblingIt can be seen that it requires an average profit that exceeds the profit obtained from reliable gambling.

## Risk aversion

A preference has an expected utility function expression by mathematical formula (1), Bernoulli utility function Is on the 2nd floorDifferentiableWe define the following as

However, Are each function Suppose that it refers to the first derivative and the second derivative of.this Bernoulli utility function about**Arrow-Platt's Absolute Risk Aversion**(British: Arrow-Pratt coefficient of absolute risk aversion), Or called Arrow-Platt's Absolute Hazard Avoidance^{[7]}^{[8]}^{[9]}^{[10]}..Sometimes referred to simply as absolute risk aversion. If is monotonically increasing and concave function Absolute risk aversion is always non-negative.

The magnitude of the absolute risk aversion of the expected utility function Arrow-Platt, which expresses a risk-averse preference, indicates how much the preference dislikes risk.That is, the Bernoulli utility function, which is a different monotonically increasing and concave function. と About its absolute risk aversion と But, If you meet The preference expressed by the expected utility function that has Bernoulli as the utility function Tends to dislike risk more than the preference expressed by the expected utility function that has Bernoulli as the utility function^{[11]}.

Similarly, the coefficient defined below**Arrow-Platt's Relative Risk Aversion**(British: Arrow-Pratt coefficient of relative risk aversion)^{[12]}^{[13]}.

## Risk-averse utility function

The following is a specific example of a utility function that expresses risk-averse preferences.

### Hyperbolic Absolute Risk Aversion (HARA) type utility function

Bernoulli utility function of an expected utility function Absolute risk aversion

When represented by, the expected utility function is**Hyperbolic Absolute Risk Aversion (HARA) type utility function**と 呼 ば れ る^{[14]}. However, Is a constant. HARA-type utility functions include many expected utility functions that express typical risk-averse preferences used in economics.Specific examples are given below.

#### Absolute risk aversion constant (CARA) type utility function

Constant in absolute risk aversion of HARA type utility function And When the expected utility function is satisfied**Absolute risk aversion constant (CARA) type utility function**(British: constant absolute risk aversion (CARA) utility) Called^{[15]}.. The Bernoulli utility function of the CARA type utility function is the positive of the following functionAffine transformationRepresented by^{[16]}.

However, Is. The absolute risk aversion of the CARA utility function is always constant Will be.The CARA type utility function is also called an exponential type utility function.

#### Relative risk aversion constant (CRRA) type utility function

Constant in absolute risk aversion of HARA type utility function And When the expected utility function is satisfied**Relative risk aversion constant (CRRA) type utility function**(British: constant relative risk aversion (CRRA) utility) Called^{[15]}.. The Bernoulli utility function of the CRRA type utility function is the positive of the following functionAffine transformationIt is represented by.

However, Is. The relative risk aversion of the CRRA utility function is always constant Will be.Also, the CRRA type utility function is At the time of the hierarchical utility function, At the time of, it is also called a logarithmic utility function.Also, gambling that can be compared with this utility function must always bring non-negative benefits.

#### Secondary utility function

nextQuadratic functionThe expected utility function with the Bernoulli utility function of is also a HARA type utility function.

However, Is a constant And the benefits of gambling that can be compared with this expected utility function Must be smaller^{[17]}.

### Mean distributed utility function

The utility function represented by**Mean distributed utility function**Call.

However, Is a positive constant.The mean distributed utility function isModern portfolio theory,Capital asset pricing modelIt is one of the utility functions that justifies the mean variance analysis in.

## footnote

**^**Mas-Colell, Whinston and Green & (1995) p.185**^**Mas-Colell, Whinston and Green & (1995) p.184**^**Ikeda & (2000) p.12**^**Mas-Colell, Whinston and Green & (1995) p.186**^**Ikeda & (2000) p.17**^**Mas-Colell, Whinston and Green & (1995) p.187**^**Mas-Colell, Whinston and Green & (1995) p.190**^**Ikeda & (2000) p.19**^**Arrow & (1951)**^**Pratt & (1964)**^**Mas-Colell, Whinston and Green & (1995) p.191**^**Mas-Colell, Whinston and Green & (1995) p.194**^**Ikeda & (2000) p.22**^**Ikeda & (2000) p.30- ^
^{a}^{b}Ikeda & (2000) p.32 **^**An expected utility function using an arbitrary Bernoulli utility function and an expected utility function using an arbitrary positive affine transformation for the Bernoulli utility function as a Bernoulli utility function express the same preference. Mas-Colell, Whinston and Green & (1995) p.173**^**Mas-Colell, Whinston and Green & (1995) p.209

## References

- Arrow, Kenneth J. (1951), “Alternative Approaches to the Theory of Choice in Risk-Taking Situations”,
*Econometrics***19**(4): 404-437, JSTOR 1907465 - Mas-Colell, Andreu; Whinston, Michael Dennis; Green, Jerry R (1995),
*Microeconomic Theory*, Oxford University Press, ISBN 9780195102680 - Pratt, John W. (1964), “Risk Aversion in the Small and in the Large”,
*Econometrics***32**(1/2): 122-136, JSTOR 1913738 - Masayuki Ikeda "Basics of Financial Economics" Asakura Shoten<Finance course>, 2000.ISBN 9784254545524.

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