Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle
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Abstract
This paper introduces an innovative framework for dynamically optimizing consumption and investment decisions by integrating a risk penalization mechanism directly into the system’s dynamics. Leveraging Forward-Backward Stochastic Differential Equations (FBSDEs), our approach enables adaptive risk regulation in response to market fluctuations. We formulate the optimization problem, analyze the associated adjoint equations, and derive explicit characterizations of optimal strategies. Numerical simulations across multiple scenarios validate the robustness of the proposed method, demonstrating a significant reduction in terminal wealth variance compared to classical approaches. Our model thus offers a promising advance in dynamic financial risk management.
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