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

By Dmitry O. Kramkov, M. Sîrbu. 2006

79 citations recorded by the source corpus.

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: \begin{tabular}@p97mm@ 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;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). \end{tabular}

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7ef93e1f42c42c17e8500d070b89c0f28f789ace

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Citations in the corpus

Asymptotic analysis of utility-based hedging strategies for small number of contingent claims (2007, methodology): “In addition, motivated by [11, 12 ], we make the following assumption on U:”
UTILITY MAXIMIZATION IN AFFINE STOCHASTIC VOLATILITY MODELS (2010, methodology): “The q-optimal equivalent martingale measure from the previous discussion is needed as a first step in the derivation of asymptotic utility-based option prices and hedging strategies according to [ 28 , 29].”
Portfolios and risk premia for the long run. (2012, background): “This observation shows that P̂ y corresponds to the long horizon limit of the probability R considered by Kramkov and Ŝırbu (2006a, 2006b, 2007) in finite horizon, in the context of sensitivity analysis pricing of option prices.”