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

Bogdan Iftimie ()
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Bogdan Iftimie: Bucharest University of Economic Studies

Journal of Global Optimization, 2023, vol. 86, issue 3, No 8, 713-739

Abstract: 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.

Keywords: Robust optimization; Power utility; Stochastic interest rate; Enlarged filtration; Minimax theorem; Dual problem; Backward stochastic differential equations with jumps (BSDEJs); 49J35; 91B16; 90C46; 90C47; 91G30; 93E20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-023-01273-0

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