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

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dc.creatorKramkov, Dmitry
dc.creatorS\^{ı}rbu, Mihai
dc.date2007-02-14
dc.date.accessioned2026-07-07T12:11:21Z
dc.date.available2026-07-07T12:11:21Z
dc.descriptionIn 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}
dc.descriptionPublished at http://dx.doi.org/10.1214/105051606000000529 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0702413
dc.identifierhttp://arxiv.org/abs/math/0702413
dc.identifierAnnals of Applied Probability 2006, Vol. 16, No. 4, 2140-2194
dc.identifierdoi:10.1214/105051606000000529
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210196
dc.subjectProbability
dc.subjectComputational Finance
dc.subject90A09, 90A10 (Primary) 90C26 (Secondary)
dc.titleSensitivity analysis of utility-based prices and risk-tolerance wealth processes
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