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arXiv · 1906.03690

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

Hyungbin Park·Stephan Sturm
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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. 2019-06-09. A sensitivity analysis of the long-term expected utility of optimal portfolios. https://arxiv.org/abs/1906.03690

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