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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.

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Degrees of Risk aversion and Expected utility

There are two agents with utility functions $g_1$ and $g_2$, where the agent with function $g_2$ has higher (absolute) risk-aversion. The agents face a lottery $((q,x_1),((1-q),x_2))$, i.e. agents ...
Ramandeep's user avatar
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Comparing agent decision-making under risk-neutrality and risk-Aversion

I am working on the following question but have not been able to come up with a suitable way to proceed. The setup is as follows: There is a technology (for example, a vaccine) which reduces the ...
Ramandeep's user avatar
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Von Neumann-Morgenstern utility and taxes

"Consider a risk-averse individual with Von Neumann-Morgenstern utility and who invests in a risky asset. If the return on the risky asset is taxed, so the consumer has an incentive to invest ...
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Estimating willingness-to-pay for a risk-averse person who can 'select' lotteries

I'm studying how the willingness-to-pay differs for individuals who can 'select' lotteries. Individuals are presented with L1 first and can pay some amount to get lottery L2. Assume these are my ...
comparing-lotteries-help's user avatar
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Mean preserving spread of a lottery

Suppose G is a lottery where the payoff is equal to -1 with 0.5 probability and 1 with 0.5 probability. I'm trying to show that G is a mean preserving spread of a lottery with uniform distribution on [...
Justin Cross's user avatar
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How do I show that it's optimal to invest in equal amount of 2 risky assets via mean-preserving spread?

Suppose a risk-averse investor with differentiable Bernoulli utility $u$ and wealth $w$ that can be allocated between asset $X$ and $Y$. Both $X,Y$ have positive expectations. If the investor invests ...
Ludwig Gershwin's user avatar
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What does the empirical literature tell us about the relative merits of alternative functional forms describing the marginal utility of income?

Among the various functional forms that have been used on model the marginal utility of income in, e.g., in making decisions under uncertainty, and perhaps intertemporal choice as well, is the ...
andrewH's user avatar
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What are the theoretical approaches to ambiguity?

I'm trying to understand the different approaches that economists took to investigate ambiguity. Two approaches particularly caught my eyes: the model by Klibanoff, Marinacci and Mukerji (2009), and ...
Eddie's user avatar
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Expected value in budget constraint

I have been reading this paper by Yang Liu, Lukas Schmid and Amir Yaron, which contains a very elegant mechanism that generates an endogenous liquidity premium for US government debt. However, I got ...
Wittgenstein's Poker's user avatar
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What does the Arrow-Pratt risk aversion measure mean in the deterministic case?

What type of preferences that are not related to risk aversion can the Arrow-Pratt measure of absolute (or relative) risk aversion model? So far, it seems to me that low RRA/ARA preferences imply that ...
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Calculate influence of absolute risk aversion on consumption decisions

Say I have the following setup: A consumer chooses between two goods $x$ and $y$ (a numeraire) such that she maximises: $$V(x,y)=u(x)+y$$ Under the constraint that her revenue $R$ is such that: $$R\...
ju_pi_car's user avatar
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If kink, is the agent risk-neutral?

If the graph has a kink, at that point would we assume the agent is risk-neutral?
aliosha karamazov's user avatar
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Risk aversion and utility transformation: are preferences still the same?

If you have two utility functions $u(\cdot), \; v(\cdot)$ such that $v(x) = f(u(x))$ for some monotonic transformation $f(\cdot)$, then $u(\cdot)$ and $ v(\cdot)$ represent the same preference ...
Joao Francisco Cabral Perez's user avatar
2 votes
1 answer
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Portfolio choice and risk aversion

Given utility function $U(w) = -e^{-w}$ of an investor (where $w$ denotes wealth) and two assets - risky and safe, will the investor's amount of investment into the risky asset be indifferent of his ...
riskyasset's user avatar
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What is the economic intuition of prudence in the static case?

How can we interpret a "prudent" agent in the static case (i.e., someone with $u'''(\cdot)>0$)? I understand that in a dynamic setting, someone exhibiting prudence would do precautionary ...
ju_pi_car's user avatar
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Does the Arrow-Pratt measure of absolute risk aversion have a lower bound with DARA utlity?

Say I have the following utility function: $$u(x,w)=f(w+x)$$ This utility exhibits decreasing absolute risk aversion ($f'>0$, $f''<0$ and $f'''>0$). $x\in R_+$ is the control variable and $w\...
ju_pi_car's user avatar
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Deriving the constant relative risk aversion utility function

Here is the question I am trying to tackle: Suppose that we are given a utility function $u$ with relative risk aversion $R_u$. Show that $R_u$ is constant and equal to $\rho$ iff there exist $\zeta\...
Philip Hartfield's user avatar
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What is the risk aversion domain and how this could change in a dynamic market game?

Most of the market microstructure theory models assume a risk aversion coefficient, say $\gamma$ that is indexed with $i$ since any individual $i$ has her own $\gamma_i$ coefficient. Also, the inverse ...
Oliver Queen's user avatar
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example of risk neutral or risk loving utility function

i"m looking for an example of either risk loving or risk neutral utility function. what i mean is like for risk averse, we have the HARA utility function. is there a utility function that exhibit ...
Oei Evelyn Clarieta Kusuma's user avatar
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CARA risk-parameter estimation for discrete data as in Holt and Laury (2002)

I have a dataset with around 40 participants who choose between a pair of lotteries A or B while the probabilities of prizes change. This setting is similar to that in Holt and Laury (2002): Risk ...
Juustomies6's user avatar
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Convergence of various forms of Prospect Theory?

I'm not a mathematician but it seems that my problem is a rather technical than an economic one, but i hope this is still the right audience. My problem is the following: I want to analyse the effects ...
T123's user avatar
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Where can I find estimates of CARA risk aversion

I'm trying to get a sense of what levels of CARA risk aversion are typically considered "reasonable" in the literature for American consumers. Can someone point me to some papers that ...
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On risk aversion and validity of utility functions

Question A risk-averse, non-satiated investor has decided to use the utility function $$U(w) = w + dw^2,$$ where $$d \leq 0$$ is a constant, to describe his preferences. The investor has a current ...
Ethan Mark's user avatar
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Experimenting with Mean Variance Analysis

here with a question about mean-variance analysis and utility theory hope you can help me. First point My main objetive is to maximize the expected utility from portfolios given by $\sigma_p^2=\frac{C}...
CobbDgls's user avatar
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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 ...
Sara's user avatar
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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, ...
Sara's user avatar
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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 ...
T123's user avatar
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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 ...
kleinerde's user avatar
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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 $w_0=60000$, $...
weldon's user avatar
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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 $\frac{1}{2}$ ...
Mrnobody's user avatar
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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 ...
James Bowery's user avatar
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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 ...
Mrnobody's user avatar
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3 answers
194 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 ...
xxgaryxx's user avatar
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1 answer
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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,...
Pelin's user avatar
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2 answers
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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); ...
capcapuccino's user avatar
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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 ...
Matifou's user avatar
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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 ...
epine_se's user avatar
1 vote
1 answer
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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 ...
Blerg's user avatar
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1 answer
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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 ...
Richard Hardy's user avatar
5 votes
1 answer
81 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, ...
Lin Jing's user avatar
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1 vote
1 answer
470 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 ...
alatriste's user avatar
3 votes
1 answer
160 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 ...
Aeeh's user avatar
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5 votes
1 answer
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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 ...
Kroko's user avatar
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1 answer
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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 ...
Biff's user avatar
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3 votes
1 answer
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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.
rickyrichboy's user avatar
2 votes
1 answer
227 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 ...
Aqqqq's user avatar
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0 answers
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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 ...
moritzthird's user avatar
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1 answer
401 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 ...
user333444's user avatar
2 votes
0 answers
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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 ...
Bayesian's user avatar
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1 vote
1 answer
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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 ...
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