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
0 votes
1 answer
49 views

Constant relative risk aversion for wealth spanning from negative to positive

I am modeling scenarios that could involve wealth for all real numbers and I am assuming constant relative risk aversion. I need to model the scenarios for different risk aversion levels, but I can't ...
user avatar
  • 115
1 vote
3 answers
47 views

risk aversion and the law of diminishing marginal utility

I see many plots where x is wealth and y is utility. If a person is risk averse, he has a concave line on the plot. If the person is risk neutral, her line on the plot is straight. On the other hand, ...
user avatar
  • 115
1 vote
0 answers
43 views

Risk Premium for Prospect Theory-like value function

I am curious how to calculate the following risk premium for a utility function that is not linear in $w$. What i'm asking is the following: Consider an agent with utility function $u$, initial wealth ...
user avatar
  • 193
1 vote
0 answers
3 views

Finding the risk attitude parameter in a CPT Risk Elicitation Model

I'm working with this article by Bauermeister et al. that compares the risk attitude parameters found using two different risk elicitation models. The models each use a series of gambling options to ...
user avatar
  • 299
0 votes
1 answer
104 views

Negative certainty equivalent

Let us consider an agent of initial wealth $w_0$ whose utility function is $u(x)=\sqrt{x}$. This individual faces a risk of loss $Z$ which occurs with probability $p$. It is assumed that $w_0=60000$, $...
user avatar
  • 1
1 vote
1 answer
47 views

certainty equivalent and lotteries [closed]

suppose an agent has $u(z)=-e^{-bz}$ where $b>0$ as her Bernoulli utility function and faces two gambles: G1: win 1000 dollars with probability $\frac{1}{2}$ and zero with probability $\frac{1}{2}$ ...
user avatar
1 vote
0 answers
16 views

Is There an rNPV Model Relating Money Supply, Total Wealth and Money Velocity?

It seems sensible that the supply of constant-value units of fiat money should roughly correspond to the total wealth of the jurisdiction's economy, in the same sense that an on-demand gold ...
user avatar
0 votes
0 answers
35 views

comparing two lotteries

Suppose the prize space (in dollars) is $\mathbb{Z}$ = {1, 2, 3, 4, 5, 6, 7, 8} and consider choices by an agent whose preferences (over lotteries) satisfy the von Neumann-Morgenstern axioms. A risk ...
user avatar
0 votes
3 answers
69 views

Why does a risk-return relationship that has historically been positive confirm risk averse investors?

As I am reading through a corporate finance textbook I came across the following figure that plots the relationship between risk and return for different asset classes: The textbook states: Figure ...
user avatar
0 votes
0 answers
47 views

In a Principal Agent Model how to demonstrate that the optimal contract is second best?

I am working with a Risk Averse Principal and Risk Neutral agent (Along the lines of the Mascolell, Whinston and Green Chapter 14 Problem Number 14.B.2). Since the Principal is risk averse so here the ...
user avatar
  • 1
1 vote
1 answer
35 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,...
user avatar
  • 13
0 votes
2 answers
59 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); ...
user avatar
2 votes
0 answers
29 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 ...
user avatar
  • 121
3 votes
0 answers
84 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 ...
user avatar
1 vote
1 answer
55 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 ...
user avatar
  • 113
2 votes
1 answer
363 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 ...
user avatar
5 votes
1 answer
68 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, ...
user avatar
  • 199
1 vote
1 answer
182 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 ...
user avatar
3 votes
1 answer
133 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 ...
user avatar
  • 33
5 votes
1 answer
55 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 ...
user avatar
  • 151
1 vote
1 answer
348 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 ...
user avatar
  • 13
3 votes
1 answer
446 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.
user avatar
1 vote
1 answer
83 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 ...
user avatar
  • 372
1 vote
0 answers
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 ...
user avatar
0 votes
1 answer
238 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 ...
user avatar
2 votes
0 answers
42 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 ...
user avatar
  • 5,090
1 vote
1 answer
253 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 ...
user avatar
  • 734
4 votes
3 answers
105 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 ...
user avatar
  • 141
-1 votes
1 answer
165 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,...
user avatar
  • 242
2 votes
1 answer
89 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) ...
user avatar
  • 23
4 votes
1 answer
170 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 ...
user avatar
  • 71
0 votes
1 answer
70 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 ...
user avatar
  • 132
6 votes
1 answer
492 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 ...
user avatar
3 votes
2 answers
292 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 $k$ ...
user avatar
  • 153
3 votes
1 answer
89 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. ...
user avatar
  • 3,730
4 votes
1 answer
119 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 ...
user avatar
  • 803
3 votes
1 answer
588 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), ...
user avatar
  • 145
1 vote
0 answers
52 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 = \...
user avatar
2 votes
1 answer
146 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% ...
user avatar
  • 63
3 votes
1 answer
7k 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 ...
user avatar
1 vote
0 answers
410 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 ...
user avatar
4 votes
1 answer
98 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. ...
user avatar
0 votes
1 answer
190 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(...
user avatar
2 votes
0 answers
673 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-...
user avatar
  • 21
7 votes
2 answers
406 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 ...
user avatar
4 votes
4 answers
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 ...
user avatar
0 votes
2 answers
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 ...
user avatar
5 votes
1 answer
53 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 ...
user avatar
  • 205
3 votes
2 answers
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 ...
user avatar
  • 6,652
13 votes
0 answers
933 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 ...
user avatar
  • 9,107