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A sensitivity analysis of the long-term expected utility of optimal portfolios

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  • Hyungbin Park
  • Stephan Sturm

Abstract

This paper discusses the sensitivity of the long-term expected utility of optimal portfolios for an investor with constant relative risk aversion. Under an incomplete market given by a factor model, we consider the utility maximization problem with long-time horizon. The main purpose is to find the long-term sensitivity, that is, the extent how much the optimal expected utility is affected in the long run for small changes of the underlying factor model. The factor model induces a specific eigenpair of an operator, and this eigenpair does not only characterize the long-term behavior of the optimal expected utility but also provides an explicit representation of the expected utility on a finite time horizon. We conclude that this eigenpair therefore determines the long-term sensitivity. As examples, explicit results for several market models such as the Kim--Omberg model for stochastic excess returns and the Heston stochastic volatility model are presented.

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  • Hyungbin Park & Stephan Sturm, 2019. "A sensitivity analysis of the long-term expected utility of optimal portfolios," Papers 1906.03690, arXiv.org.
    • Handle: RePEc:arx:papers:1906.03690
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    File URL: http://arxiv.org/pdf/1906.03690
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    Cited by:

    1. Hyungbin Park, 2021. "Influence of risk tolerance on long-term investments: A Malliavin calculus approach," Papers 2104.00911, arXiv.org.
    2. Hyungbin Park, 2019. "Convergence rates of large-time sensitivities with the Hansen--Scheinkman decomposition," Papers 1912.03404, arXiv.org, revised Jan 2021.

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