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

Sahar Albosaily () and Serguei Pergamenchtchikov ()
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Sahar Albosaily: University of Hail, Hail, Saudi Arabia
Serguei Pergamenchtchikov: LMRS - Laboratoire de Mathématiques Raphaël Salem - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - CNRS - Centre National de la Recherche Scientifique

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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: Feynman-Kac mapping; Hamilton-Jacobi-Bellman equation; Itô formula; Brownian motion; Ornstein-Uhlenbeck processes; stochastic processes; financial markets; spread markets; optimality (search for similar items in EconPapers)
Date: 2021-11-29
Note: View the original document on HAL open archive server: https://hal.science/hal-05723569v1
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Published in Stats, 2021, 4 (4), pp.1012-1026. ⟨10.3390/stats4040058⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05723569

DOI: 10.3390/stats4040058

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