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Questions tagged [utility-theory]

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0
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1answer
47 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 ...
-2
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1answer
125 views

Implicit relation between risk and reward

I want to differentiate w.r.t. $\sigma^2$ the following equation $u'(Y)\mu$ + $\frac{u''(Y)}{2}$$(\sigma^2 + \mu^2) = 0$ where we can consider $\mu$(reward) as an implicit function of $\sigma^2$(risk) ...
17
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0answers
184 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 $Q-$ ...
5
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0answers
93 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 ...
4
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0answers
137 views

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 ...
3
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0answers
32 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 ...
3
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0answers
82 views

Why is utility concave?

I have read that the utility function is usually concave. I assume this requirement arises in order to meet the diversification effect:$$f(\lambda_1c_1+\lambda_2c_2)\ge \lambda_2 f(c_1)+\lambda_2f(c_2)...
1
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0answers
37 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 ...
1
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0answers
49 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, ...
1
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0answers
20 views

Reference request: Terminal wealth distribution including deterministic contribution

I'm looking into some classical utility maximization problems. In particular, I'm interested in looking at the wealth evolution where you invest your money across $n$ assets and each time period you ...
1
vote
0answers
30 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?
1
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0answers
210 views

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 ...
1
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0answers
61 views

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 ...
1
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0answers
97 views

optimizing the expected utility

The market consist of one single stock and call options with different strike price based on the given stock.Suppose the market believes the stock follows the following GBM:$$dS_t=\mu S_tdt+\sigma ...
1
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0answers
67 views

Financial theory

Ok guys, I'm studying from Danthine and Donaldson - Intermediate Financial Theory. The book itself doesn't have a lot of worked examples, and I'm lacking the basics for understanding some concepts ...
1
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0answers
51 views

Comparing cost of two alternative given their distribution

I have distribution for cost of two alternative through Monte Carlo simulation. The distributions are not normal. Given the benefit of the two alternatives is the same but ungiven, I want to choose ...
0
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0answers
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 ...
0
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0answers
314 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 ...