Dynamic intertemporal utility optimization by means of Riccati transformation of Hamilton-Jacobi Bellman equation

Sona Kilianova and Daniel Sevcovic

Papers from arXiv.org

Abstract: 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.

Date: 2019-03
New Economics Papers: this item is included in nep-dge and nep-upt
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1903.10065

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