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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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 [...
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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 ...
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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 ...
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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
...
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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 ...
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What does the Arrow-Pratt risk aversion measure means 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:
$$R\...
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If kink, is the agent risk-neutral?
If the graph has a kink, at that point would we assume the agent is risk-neutral?
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Risk aversion and utility transformation: are preferences still the same?
If you have two utility functions $u(\cdot), \; v(\cdot)$ such that $v(x) = f(u(x))$ for some monotonic transformation $f(\cdot)$, then $u(\cdot)$ and $ v(\cdot)$ represent the same preference ...
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Portfolio choice and risk aversion
Given utility function $U(w) = -e^{-w}$ of an investor (where $w$ denotes wealth) and two assets - risky and safe, will the investor's amount of investment into the risky asset be indifferent of his ...
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What is the economic intuition of prudence in the static case?
How can we interpret a "prudent" agent in the static case (i.e., someone with $u'''(\cdot)>0$)?
I understand that in a dynamic setting, someone exhibiting prudence would do precautionary ...
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Does the Arrow-Pratt measure of absolute risk aversion have a lower bound with DARA utlity?
Say I have the following utility function:
$$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\...
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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\...
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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 ...
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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 ...
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Hyperbolic absolute risk aversion
i'm having problem understanding what makes a utility function is part of HARA? and why is a utility function is not part of HARA and what is the example of a non HARA function?
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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 ...
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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 ...
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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 ...
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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}...
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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 ...
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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, ...
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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 ...
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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 ...
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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$, $...
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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}$ ...
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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 ...
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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 ...
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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 ...
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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,...
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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); ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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,...
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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) ...
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