2019/06/09 by Hyungbin Park, Park, Hyungbin, Stephan Sturm +1
Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1906.03690
arxiv created 2019/06/09 · openalex publication_date 2019/06/09 · arxiv updated 2019/06/11 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
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.