2015/04/15 by Gregor Heyne, Heyne, Gregor, Michael Kupper +3
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Dual (grammatical number) #Duality (order theory) #Economic theories and models #Economics #Finance #Financial Markets and Investment Strategies #Mathematical economics #Mathematical optimization #Mathematics #Maximization #Optimal control #Optimization problem #Portfolio #Pure mathematics #Regular polygon #Saddle #Saddle point #Stochastic control #Stochastic processes and financial applications #Utility maximization #Utility maximization problem #math.OC #msc:60H20 #msc:91B16 #msc:91G10 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1504.03931
arxiv created 2015/04/15 · openalex publication_date 2015/04/15 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This paper studies the utility maximization problem of an agent with non-trivial endowment, and whose preferences are modeled by the maximal subsolution of a BSDE. We prove existence of an optimal trading strategy and relate our existence result to the existence of a maximal subsolution to a controlled decoupled FBSDE. Using BSDE duality, we show that the utility maximization problem can be seen as a robust control problem admitting a saddle point if the generator of the BSDE additionally satisfies a specific growth condition. We show by convex duality that any saddle point of the robust control problem agrees with a primal and a dual optimizer of the utility maximization problem, and can be characterized in terms of a BSDE solution.