Discrete time portfolio optimisation managing value at risk under heavy tail return distribution

Abstract

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximise his expected utility of the portfolio subject to the value at risk assuming a heavy tail distribution of the stock price return. We use Markov decision process and dynamic programming principle to get the optimal strategies and the value function which maximise the expected utility for parametric as well as non-parametric distributions. Due to lack of explicit solution in the non-parametric case, we use numerical integration for optimisation. The highlights of the study are used Markov decision process and dynamic programming to get recursive relation for optimal strategy of known distribution. Once it approaches the terminal position, we will build-up more on the risky asset or will liquidate the risky asset. In the non-parametric case, we used numerical integration to find the recursive relation for optimal strategy. In this case, the value function we obtained has wide range of fluctuations and the same is also true for the portfolio wealth.