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

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 s...

Full description

Saved in:
Bibliographic Details
Published inJapan journal of industrial and applied mathematics Vol. 36; no. 2; pp. 497 - 519
Main Authors Kilianová, Soňa, Ševčovič, Daniel
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.07.2019
Springer Nature B.V
Subjects
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Economic models
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical analysis
Numerical methods
Optimization
Original Paper
Transformations (mathematics)
Traveling waves
Finite volume scheme
70H20
Dynamic stochastic portfolio optimization
Dynamic utility
Hamilton–Jacobi–Bellman equation
91B16
91B70
90C15
Riccati transformation
35K55
34E05
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-019-00349-3