Stochastic control methods for optimization problems in Ornstein-Uhlenbeck spread models

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 develop stochastic optimal control methods for spread financial models defined by the Ornstein-Uhlenbeck (OU) processes. To this end, we study the Hamilton -Jacobi -Bellman (HJB) equation using the Feynman -Kac (FK) probability representation. We show an existence and uniqueness theorem for the classical solution of the HJB equation, a quasi-linear partial derivative equation of parabolic type. Then we show a special verification theorem and, as a consequence, construct optimal consumption/investment strategies for power utility functions. Moreover, using fixed point tools we study the numeric approximation for the HJB solution and we establish the convergence rate which, as it turns out in this case, is super geometric, i.e., more rapid than any geometric one. Finally, we illustrate numerically the behavior of the obtained strategies.

Keywords: Stochastic control; Stochastic differential equations; Dynamical programming; Hamilton-Jacobi-Bellman equation; Feynman -Kac mapping; Financial spread markets (search for similar items in EconPapers)
Date: 2023-08-23
Note: View the original document on HAL open archive server: https://hal.science/hal-05723578v1
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Published in Journal of Mathematical Analysis and Applications, 2023, 530, ⟨10.1016/j.jmaa.2023.127668⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05723578

DOI: 10.1016/j.jmaa.2023.127668

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