# Questions tagged [utility-theory]

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### 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 ...
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### CRRA Utility Function Problem

"Assume an investor with total wealth of $100 that has a constant relative risk aversion (CRRA) utility function. The functional formula for the CRRA utility function is given as$\ U[W]=\frac{W^{1-θ}...
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### Does CRRA-utility imply higher risk-aversion for lower wealth?

Consider the utility function $u(W)=\dfrac{1}{1-\gamma}W^{1-\gamma}$, where $\gamma=0.5$ Since this function will exhibit decreasing marginal utility of wealth, is it correct to say that for any ...
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### Debreu's Representation Theorem proof

In microeconomy this theorem states that : given a consumption set $X\subseteq\mathbb{R}^n$, if the preference relation $\succcurlyeq$ is complete, transitive and continuous there exist a utility ...
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### Finding parameters of an utility function in a market making strategy to apply it in practice

I am reading this paper below about optimal bid-ask spread in a market making strategy. It finds an approximation for optimal solution, but I cannot understand how it's practice to set the parameters ...
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### How to derive Expected utility approximation with power function

My question concern how to derive the expected utility of a power function in the following model: I have two normally distributed risky assets X and Y and a risk-free asset B, for which : rA = 0.5y ...
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### Martingale method for utility maximization - is the optimal strategy also a martingale?

The Martingale Method for utility maximization (seen in e.g. Björk's book) is based on separating the optimization problem $E^\mathbb{P}[U(X_T)]$ over a class of admissible strategies into the static ...
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### List of risk-averse utility functions

In the context of optimal portfolio allocation, I am looking for a (possibly exhaustive) list of risk-averse utility functions verifying part of the so-called Inada conditions. Essentially, I am ...
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### Explain Four Basic Axioms of Maximising Expected Utility

I begin learn PRM , Someone help me understand Four Basic Axioms of Maximising Expected Utility most intuitive way .Thank you very much
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### example Hamilton-Jacobi-Bellman Equation - clarification of $dX_t$ derivation using $\pi_t$, $\Pi_t$

I have a market with safe rate r and risky asset S $$\frac{dS_t}{S_t}=(r+Y_t)dt+\sigma dW_t \quad \quad (1)$$ $$dY_t = - \lambda Y_t +dB_t \quad \quad (2)$$ where W, B are Brownian Motions with ...
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### Validity of CAPM

I came across some literature regarding "Framing Theory" or "Prospect Theory", and the validity of CAPM. I was wondering if you could shed some light on a few questions I have in this regard: ...
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### Why maximize expected growth rate?

It seems to me that the optimality of the Kelly Criterion relies on the assumption that it is in an investor's best interest to maximize his portfolio's expected growth rate. Why would he care what ...
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### Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?

Or simply: why do we call equivalent martingale measures as risk-neutral measures? In the utility or game theory, when we consider a person's preferences to certain outcomes, we often deal with the ...
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### Critique against consumption-based asset pricing theory?

I find asset pricing theory very vague and full of assumptions, especially the consumption-based modern theory. In its essence, the theory states that asset prices depend on the covariance between ...