Optimal Investment and Consumption for Multidimensional Spread Financial Markets with Logarithmic Utility

Sahar Albosaily and Serguei Pergamenchtchikov
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Sahar Albosaily: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia
Serguei Pergamenchtchikov: Laboratoire de Mathématiques Raphael Salem, UMR 6085 CNRS-Université de Rouen, F76801 Saint-Étienne-du-Rouvray, France

Stats, 2021, vol. 4, issue 4, 1-15

Abstract: We consider a spread financial market defined by the multidimensional Ornstein–Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions using a stochastic dynamical programming method. We show a special verification theorem for this case. We find the solution to the Hamilton–Jacobi–Bellman (HJB) equation in explicit form and as a consequence we construct optimal financial strategies. Moreover, we study the constructed strategies with numerical simulations.

Keywords: optimality; Feynman–Kac mapping; Hamilton–Jacobi–Bellman equation; Itô formula; Brownian motion; Ornstein–Uhlenbeck processes; stochastic processes; financial markets; spread markets (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:4:y:2021:i:4:p:58-1026:d:690503

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