Stability of the Exponential Utility Maximization Problem with Respect to Preferences

30 Pages Posted: 15 Jan 2017

See all articles by Hao Xing

Hao Xing

London School of Economics & Political Science (LSE)

Date Written: January 2017

Abstract

This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on converges to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal payoffs, and optimal investment strategies are obtained, their rate of convergence is also determined. Stability of utility‐based pricing is studied as an application. Second, a sequence of utilities defined on converges to the exponential utility after shifting and scaling. Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in [Nutz, M. (2012): Risk aversion asymptotics for power utility maximization. Probab. Theory & Relat. Fields 152, 703–749], which establishes the convergence for a sequence of power utilities.

Keywords: utility maximization, exponential utility, stability, semimartingales, utility‐based prices

Suggested Citation

Xing, Hao, Stability of the Exponential Utility Maximization Problem with Respect to Preferences (January 2017). Mathematical Finance, Vol. 27, Issue 1, pp. 38-67, 2017. Available at SSRN: https://ssrn.com/abstract=2899163 or http://dx.doi.org/10.1111/mafi.12073

Hao Xing (Contact Author)

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

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