Dynamic portfolio choice under the time-varying, jumps, and knight uncertainty of asset return process

Abstract

By introducing a stochastic element to the double-jump diffusion framework to measure the Knight uncertainty of asset return process, this paper builds the model of dynamic portfolio choice, which maximizes the expected utility of terminal portfolio wealth. Through specifying the state function of uncertainty-aversion, it utilizes the max-min method to derive the analytical solution of the model to study the effect of the time-varying, jumps, and Knight uncertainty of asset return process on dynamic portfolio choice and their interactions. Results of comparative analysis show: The time-varying results in positive or negative intertemporal hedging demand of portfolio, which depends on the coefficient of investor’s risk aversion and the correlation coefficient between return shift and volatility shift; the jumps in asset return overall reduce investor’s demand for the risky asset, which can be enhanced or weakened by the jumps in volatility; due to the existing of the Knight uncertainty, the investor avoids taking large position on risky asset, and the resulting is the improving of portfolio’s steady and immunity. At last, an empirical study is done based on the samples of Shanghai Exchange Composite Index monthly return data from January 1997 to December 2009, which not only tests the theoretical analysis but also demonstrates that the proposed method in the paper is useful from the aspect of portfolio’s equivalent utility.