The Annals of Applied Probability

Sensitivity analysis of utility-based prices and risk-tolerance wealth processes

Dmitry Kramkov and Mihai Sîrbu

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In the general framework of a semimartingale financial model and a utility function U defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a “small” number of random endowments. We show that this linear approximation has some important qualitative properties if and only if there is a risk-tolerance wealth process. In particular, they hold true in the following polar cases:

1. for any utility function U, if and only if the set of state price densities has a greatest element from the point of view of second-order stochastic dominance;

2. for any financial model, if and only if U is a power utility function (U is an exponential utility function if it is defined on the whole real line).

Article information

Ann. Appl. Probab., Volume 16, Number 4 (2006), 2140-2194.

First available in Project Euclid: 17 January 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90A09 90A10
Secondary: 90C26: Nonconvex programming, global optimization

Utility maximization incomplete markets risk-aversion risk-tolerance random endowment contingent claim hedging utility-based valuation stochastic dominance


Kramkov, Dmitry; Sîrbu, Mihai. Sensitivity analysis of utility-based prices and risk-tolerance wealth processes. Ann. Appl. Probab. 16 (2006), no. 4, 2140--2194. doi:10.1214/105051606000000529.

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