Questions tagged [risk-aversion]

A property of preferences that causes an agent to prefer alternatives whose outcomes are relatively certain, even when the associated expected payoff is lower.

Filter by
Sorted by
Tagged with
1
vote
1answer
32 views

Indifference between 2 risky asset

Consider the problem of an individual that must choose how much of his initial wealth w0 > 0 to allocate to a risky asset X. The risky asset X has n ≥ 2 possible return rates, namely r1, . . . , rn,...
0
votes
2answers
58 views

Can we model risk with only probability?

Sorry for the confusion! I am adding an example to see if it helps: For example, consider a gamble A, with payoffs {a,b,c,d}, whose probability of each payoff being realized is equal (so 25% each); ...
2
votes
0answers
27 views

Intuition on cumulative prospect theory, based on equi-probable outcomes?

I am trying to build my intuition on the weighting/decision function in cumulative prospect theory. I have a hard time getting a clear picture for even the simple case of equi-probabilities. Assume ...
3
votes
0answers
69 views

How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?

Statement: Let the dynamics of wealth of the agent satisfy $$dX_{t} = \pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$ where $(\pi,c)$ is an ...
0
votes
0answers
18 views

What is the math behind the coefficient of Absolute Risk aversion? [duplicate]

I have a good grasp of Calculus but I have never used the ratio of second and first derivatives. So, I am having a hard time understanding what it does and how?
1
vote
1answer
49 views

Risk with unknown probability distribution of the outcomes

From Wikipedia: "Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation and it is defined by the preference between a risky alternative ...
0
votes
0answers
18 views

Decreasing performance pay in the risk-aversion of the principal

What is the intuition behind a decreasing performance pay ß if both principal and agent are risk averse compared to a principal being risk neutral and an agent being risk averse? Actually, intuitively ...
2
votes
1answer
238 views

Examples of risk-neutral firms or people in business

I am looking for examples of approximately risk-neutral firms or people in business. Is there an industry where risk-neutrality is common for some agents (firms or people)? Are there perhaps time ...
5
votes
1answer
62 views

What does it mean by saying someone is “effectively risk averse/loving”?

Recently I am reading a paper by Ortner & Chassang (2018) on corruption control. It is a nice paper to read, and the idea is kinda cool. The game is as follows. There are 3 players, a principle, ...
0
votes
1answer
80 views

Risk neutral probability for each of 3 states

I need help to find the risk-neutral probability for states 1,2 and 3 I have two stocks: A and B. The price of A today is 180 and in a year it will be worth 288 (S1), 180 (S2) or 120 (S3); The ...
3
votes
1answer
116 views

Diminishing mariginal utility and risk preferences

Diminishing marginal utility is a concept only in cardinal utility theory rather than ordinal utility theory. As diminishing marginal utility implies a concave shape of the utility function, does it ...
5
votes
1answer
53 views

Could anyone here be able to explain gambling addiction and its debt with Microeconomics theory?

I am a research master student in Cognitive and Clinical Neuroscience, with the specialization/track Neuroeconomics and have to come up with a master thesis subject soon. I was thinking about gambling ...
1
vote
1answer
274 views

How to calculate the degree of risk aversion of a consumer in a lottery?

To give an example, say we start with 100 dollars and we enter a lottery. With probability $\pi$, this 100 dollars is reduced by 2 dollars. Otherwise our endowed 100 dollars does not change. Let's say ...
3
votes
1answer
324 views

Why is the risk premium always positive for risk averse individuals?

I think this has to do with the definition of concavity and the fact that a risk averse person has a concave utility function, but I'm not sure how that helps.
1
vote
1answer
50 views

How is the utility function with constant relative risk-aversion obtained?

In this slide, it says that constant relative risk-Aversion utility function have this form. $u(x) = \frac{1}{1-b} x^{1-b}$ for $b≠1$ $u(x) = In(x)$ for $b=1$ When I tried to derive the utility ...
1
vote
0answers
60 views

Assessing risk in a decision problem with repeated toss

The problem starts at time t0. At each time step, the participant can choose to opt out and claim a loser's reward Rl. At each time step, the participant has a probability p to win a winner's reward ...
0
votes
1answer
184 views

Proof: Risk averse; Certainty Equivalent smaller than expected value

I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds: The certainty equivalent, $CE(\cdot)$, is ...
2
votes
0answers
33 views

Dominated lotteries in CPE

I have been looking into expectation-based loss aversion following Kőszegi-Rabin (2005, 2007). In particular, I find their choice-acclimating personal equilibrium (CPE) interesting, but it has a ...
1
vote
1answer
212 views

Constant absolute risk aversion and certainty equivalent

I need to prove that Constant Absolute Risk Aversion (CARA) is equivalent to \begin{gather} \int u'(x)dF(x) = u'(c(F,u)) \end{gather} where $u(x)$ is a Bernoulli utility function, $F$ is the ...
4
votes
3answers
98 views

Can I recreate an experiment on Allais paradox using student grades as payoffs?

For a project in experimental economics, I thought of doing something related to expected utility theory/prospect theory, but using grades instead of money. Is this reformulation of the Allais ...
-1
votes
1answer
153 views

Investor's optimization problem with risk aversion

Consider an investor with initial wealth $w$ and has to decide how to invest it. There is a riskless asset with rate of return $r$. The risky asset has return $x_i$ with probability $\pi_i$ for $i=1,2,...
2
votes
1answer
77 views

Construct utility function for a risk-averse agent

I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) ...
4
votes
1answer
159 views

Relative risk aversion, a property of period or lifetime utility

This question is to be understood in the context of consumption based asset pricing. I'm wondering whether relative risk aversion is a property of the period utility function, which is simply a ...
0
votes
1answer
57 views

Value of Statistical Life and Risk

I have been reading a paper by Bove & Elia (2011), where they quote a definition of the value of statistical life from Bellavance, Dionne & Lebeau (2009). I have tried making my peace with the ...
6
votes
1answer
461 views

Why is the Marginal Utility of losses deminishing in Prospect Theory?

This is Kahneman's value-plot on prospect theory: QUESTION: Why is the Marginal Utility of losses deminishing? CONTEXT: I fully understand that the Marginal Utility of gains deminishes: 100 dollar ...
3
votes
2answers
260 views

a risk lover agent preferences and the preference of risk natural agent may be the same

Consider two lotteries $N$ and $M$. Agent $i$ is risk-averse and prefers $N$. Agent $j$ is risk-neutral and prefers $M$. Would any risk-loving agent $k$ also prefer $M$? That is, would $j$ and $k$ ...
3
votes
1answer
81 views

Entrepreneurs and risk aversion

The are various opinion whether entrepreneurs are more or less risk-averse than the general population. The commonly held belief is that they are less so, but the contrary opinion exists as well. ...
4
votes
1answer
108 views

Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$. Are there intuitive interpretations of the numerical values of these ...
3
votes
1answer
547 views

Proving that constant absolute risk aversion and relative risk aversion implies independence of initial wealth

I was able to prove that for a portfolio with one risk-free asset and one risky asset, if the Arrow-Pratt measure of absolute risk aversion is constant (i.e., constant absolute risk aversion, CARA), ...
1
vote
0answers
51 views

Terminology for separability in price and value

Take an agent with mean-variance utility over something that is uncertain: $$ U(x) = \mu_x^\theta - \sigma_x^\lambda $$ $A\in \{0,1\}$ happens if $U(x)>0$, and $x$ is a random variable $$ A = \...
2
votes
1answer
126 views

CARA Coefficient Calculation

Consider the following scenario: A consumer with CARA (constant absolute risk aversion) claims that she is indifferent between "getting $2400 for sure" and "getting $5000 or $0, each with 50% ...
3
votes
1answer
6k views

von-Neumann-Morgenstern v. Bernoulli Utility Function

A great deal of time is spent distinguishing the big $U$ (von-Neumann-Morgenstern)v. small $u$ (Bernoulli Utility Function). The v.NM function maps from the space of lotteries to real number as it ...
1
vote
0answers
360 views

How a utility function which is both DARA and CRRA can be explained?

I'm studying risk aversion and I cannot make a intuitive explain about the utility function which is DARA and CRRA. for instance, let's say, $\ln W$, where $W$ stands for one's wealth. by the ...
4
votes
1answer
94 views

Testing if one regressor is a proxy for another

I'm reading Guiso, Sapienza and Zingales: "Trusting the Stock Market" The Journal of Finance, Vol. 63, No. 6, 2008 and have a question about how they test whether trust is a proxy for risk aversion. ...
0
votes
1answer
187 views

Is car accident/theft a fair bet? [closed]

A person with a current wealth of 100,000 who faces the prospect of a 25% chance of losing his or her 20,000 automobile through theft during the next year. Since there is no upside to this event and E(...
2
votes
0answers
627 views

Certainty Equivalents and Risk Premiums in Expected Utility Theory for Asymmetric Distributions

I want to calculte risk-premiums in order to assess how much risk-averse customers would be willing to pay for an insurance against an uncertain loss modeled by a random variable $X$. How would a risk-...
7
votes
2answers
387 views

Why should the statistical value of life exist?

In areas such as insurance pricing and government policy analysis, it is often necessary to assign human life a monetary amount in order to compare it with other monetary amounts. So economists have ...
3
votes
4answers
6k views

Does decreasing marginal utility imply risk aversion?

Unless I misunderstood something, seems like risk aversion and decreasing marginal utility is the same thing in the utility model, but intuitively, it seems entirely possible that an individual with ...
0
votes
2answers
1k views

Negative expected value; risk neutral choice

Suppose there are two options: (1) take a gamble with 50% chance you win \$100 and 50% chance you lose \$110 or (2) don't take the gamble at all and win/lose nothing. Would the risk-neutral take the ...
5
votes
1answer
52 views

given someone's past investing history, is there a way to calculate his risk aversion?

given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk ...
3
votes
2answers
3k views

Is DARA utility implying CRRA most of the time?

The Wikipedia page on risk aversion states that a "Constant Relative Risk Aversion implies a Decreasing Absolute Risk Aversion, but the reverse is not always true". Let me decompose this statement in ...
13
votes
0answers
844 views

How do I compute the relative risk aversion of Epstein-Zin preferences?

$$ \newcommand{\E}{\mathbb{E}} $$ Preface This question is related to this one about the elasticity of intertemporal substitution and this one about the definition of absolute risk aversion. (It's ...
4
votes
2answers
2k views

Risk Premium in the Expected Utility Theory

Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have $$ Eu(w+x) = u(w+E(x)-R). $$ The classical derivation ...
4
votes
1answer
116 views

What behaviour do different values of Relative Risk Aversion imply?

What behaviour does it imply that Relative Risk Aversion of consumption, say R(c) is less than 1, equal to 1 or greater than 1? I am reading an article of Diamond & Dybvig (1983), about Bank ...
6
votes
1answer
355 views

Does vNM rationality depend on the good chosen?

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
3
votes
1answer
284 views

Relative risk aversion and lotteries exercise

Given a consumer with a utility function, $u(w)$, and a wealth of $w>1000$. Assuming that the consumers relative risk aversion is constant and equal to 1, that is $R_r(w)=1$ for $w>0$, the ...
3
votes
1answer
3k views

Derivation of Arrow-Pratt risk aversion measure

This is a question about the derivation of Arrow-Pratt relative risk aversion measure $R(w)=-\dfrac{U^{''}(w)}{wU^{'}(w)}$. I have an own way to derive it, but I really want how did the authors ...
5
votes
3answers
1k views

Question about the Ellsberg Paradox in Expected Utility Theory

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
9
votes
3answers
1k views

Does risk aversion cause diminishing marginal utility, or vice versa?

Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
5
votes
2answers
989 views

Can a risk-averse agent's Certainty Equivalent be lower than the lowest possible outcome of a gamble?

Suppose there is an agent who faces the following gamble g: 50\$ with probability 1/3 100\$ with probability 1/3 150\$ with probability 1/3 Clearly, the E[g] = 100\$. Since agent is risk averse, we ...