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:
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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;
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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{1169065220,
author = {Kramkov, Dmitry and S\^\i rbu, Mihai},
title = {Sensitivity analysis of utility-based prices and risk-tolerance wealth processes},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 2140-2194},
language = {en},
url = {http://dml.mathdoc.fr/item/1169065220}
}
Kramkov, Dmitry; Sîrbu, Mihai. Sensitivity analysis of utility-based prices and risk-tolerance wealth processes. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 2140-2194. http://gdmltest.u-ga.fr/item/1169065220/