# Questions tagged [utility-theory]

The tag has no usage guidance.

64 questions
Filter by
Sorted by
Tagged with
103 views

### How to evaluate the following integral?

I stumbled across an expression and I wonder how to evaluate this: $-\int_ {0} ^ {+\infty} {v(x)} dw^{+} (1-p(x))$ where $v(x)$ is some utility function and $w(p(x))$ is a decision weighting function,...
37 views

66 views

### How do I maximize my expected utility of wealth?

Suppose I have a utility function say $U(p)=p^{1/2}$ and I bet on a basketball game. I have my initial investment, payouts and probabilities of winning, how can I determine the maximum I need to bet ...
41 views

### Closed Form Solution for Implied Risk Aversion with Two Assets under Quadratic Utility

So I believe there should be a closed form solution for implied risk aversion for two assets but I'm not sure how to get there. Say you have Quadratic Utility $U$ on a fully invested portfolio of two ...
252 views

### Fixes of quadratic utility when probability of decreasing utility is large

In finance and specifically portfolio theory, a popular utility function is quadratic utility $$u(x)=x-\frac{\lambda}{2}(x-\mu_X)^2$$ where $x$ is wealth and $\lambda$ is the parameter of risk ...
129 views

### Prove that the portfolio that maximizes utility lies on the efficient frontier

When maximizing mean-variance utility in a portfolio optimization framework $max \{R - \lambda \sigma ^2\}$ where R is portfolio return, $\lambda$ is a risk aversion parameter, and $\sigma^2$ is ...
30 views

### Compute Utility From Portfolio Holdings Over Time

I have a dataset comprising daily stock holdings for individual investors over a one year-period. I only know about the individuals' investment in stocks. I have no information on any other wealth of ...
126 views

### Risk-aversion parameters estimation in utility functions

Are there any "typical" risk-aversion parameters for power utility function and exponential utility function? Once I've seen an articel, in which author stated that for extremely risky person gamma in ...
123 views

### Utility-based portfolio optimization

I think I can't get the idea of optimization based on utility. For some reasons, I should choose one of several common utility functions (exponential, isoelastic function and some others). Obviously, ...
88 views

### Risk neutrality coherence with risk aversion

I haven't been able to find an understandable explanation why the risk neutrality is coherent with the risk aversion implication of the expected utility hypothesis. I can see that when using the risk ...
272 views

### Merton's portfolio problem with constraints

Suppose the investor can invest in a Black-Scholes market with one risky asset $S$ with drift $\alpha$ and volatility $\sigma$ and a riskless asset $B$ with a riskless rate of return $r$, and the ...
39 views

### Utility Maximization on a finite Probability Space. Possible mistakes in a paper?

I am currently reading this paper on utility maximization in a financial market model. On page 5 the author starts with the case of a finite probability space and on page 19 he considers the ...
441 views

### Is there a relationship between Risk Neutral Pricing framework and Nash Equilibria?

Based on the Fundamental Theorem of Asset Pricing, the risk neutral price of a contingent claim on an asset in a liquid, arbitrage free market can be determined by switching to an equivalent $Q-$ ...
297 views

### Is positive skewness preferences rational or irrational?

Is positive skewness preference rational or irrational? I have a great trouble understanding why investors should prefer positive skewness over negative one. Sometimes it is argued that preference ...
36 views

### Hedger's utility function associated with minimizing value at risk

What must be the general shape of a hedger's utility function if the hedger is minimizing value at risk? What is a simple example of such a utility function?
672 views

106 views

### Utility-optimal leverage with costs

Say I have a portfolio, $X_t$, using a leverage of $f$, such that the dynamics are given by \begin{equation} dX_t = \mu f X_t dt + \sigma f X_t dW_t \end{equation} I want to optimize the expected ...
848 views

### Are Insurance and Risk premium totally different?

I've been studying various aspects of utility function and I came across the definition of risk premium and insurance, which are mathematically very different from each other. In the book "Theory of ...
708 views

### Examples of risk-seeking utility functions?

In the past, most literature assumed a risk-averse investor to model utility preferences. This includes the CRRA and CARA utility functions. In recent papers, researchers state that investors may be ...
134 views

### Utility function for avoiding investment

An investor has initial wealth $30000$ and utility function $\ln{x}$. He is planning to invest in a project where he has $60%$ chance of gaining $\alpha%$ and $40%$ chance of losing $\beta%$. Express ...
120 views

2k views

### Utility Theory - Certainty equivalent approximation formula derivation

I have a question on an exercise from chapter 9 of D. Luenberger, Investment Science, International Edition, where I suspect there may be a typo. Exercise 8 (Certainty approximation) There is a ...
3k views

### Utility Theory - How to show that this exponential utility function is wealth-independent?

I have a question on the following exercise from chapter 9 of D. Luenberger, Investment Science, International Edition. Exercise 2 (Wealth Independence) Suppose an investor has exponential utility ...
178 views

### How to arrive at expectation of negative utility function via Taylor series expansion

I'm attempting to follow an author's steps in an argument and having trouble seeing how Taylor series expansion can be applied to give the stated result. The scenario is as follows. The mid price ...
261 views

### Investor choice problem

Guys I'm stuck with a problem... Consider the portfolio choice problem of a risk-averse individual with a strictly increasing utility function. There is a single risky asset, and a risk free asset. ...