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A robust investment-consumption optimization problem in a switching regime interest rate setting

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Abstract

In this paper we are dealing with a robust investment-consumption optimization problem in an incomplete market with a switching regime stochastic interest rate. Our methodology combines duality approach with stochastic control techniques (applied to the dual problem) specific to a non-Markovian setting, such as dynamic programming principle (initiated in Karoui and Quenez (SIAM J Control Optim 33(1):29–66, 1995)) and Backward Stochastic Differential Equations (BSDEs) theory. An auxiliary dual problem is established by means of infinite-dimensional convex duality. We derive explicit formulas for the optimal trading strategy and consumption rate in terms of the solution of some nonstandard BSDE with jumps. Links to other significant results in the domain are also provided.

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Acknowledgements

I wish to express my deepest gratitude to Monique Jeanblanc for giving me the opportunity to join Laboratoire de Mathématiques et Modélisation, Université d’Evry-Val d’Essonne for a short research visit, and also for all the support she provided to me constantly elaboration of this manuscript.

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  1. Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 1st district, 010374, Bucharest, Romania

    Bogdan Iftimie

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Correspondence to Bogdan Iftimie.

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This research was supported by Chaire risque de crédit, French Banking Federation for a short research visit at Université d’Evry-Val d’Essonne in september 2013 and by the research contract ID-303/5.10.2011. The author declares that the data supporting the findings of this study are available within the article.

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Iftimie, B. A robust investment-consumption optimization problem in a switching regime interest rate setting. J Glob Optim 86, 713–739 (2023). https://doi.org/10.1007/s10898-023-01273-0

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