2019/03/24 by Sona Kilianova, Kilianova, Sona, Daniel Sevcovic +1
Economics, Econometrics and Finance · #Dynamic stochastic portfolio optimization #Dynamic utility #FOS: Economics and business #Finite volume scheme #Hamilton-Jacobi-Bellman equation #Portfolio Management (q-fin.PM) #Riccati transformation #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1903.10065
arxiv created 2019/03/24 · arxiv updated 2019/03/26
In this paper we investigate a dynamic stochastic portfolio optimization problem involving both the expected terminal utility and intertemporal utility maximization. We solve the problem by means of a solution to a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) equation. We propose the so-called Riccati method for transformation of the fully nonlinear HJB equation into a quasi-linear parabolic equation with non-local terms involving the intertemporal utility function. As a numerical method we propose a semi-implicit scheme in time based on a finite volume approximation in the spatial variable. By analyzing an explicit traveling wave solution we show that the numerical method is of the second experimental order of convergence. As a practical application we compute optimal strategies for a portfolio investment problem motivated by market financial data of German DAX 30 Index and show the effect of considering intertemporal utility on optimal portfolio selection.