Cash flow optimization in uncertain environments: forward backward stochastic differential equation approach with pontryagin's maximum principle
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2025-01-30 https://doi.org/10.14419/2frsms38
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FBSDE; Cash Flow Optimization; Financial Risk; Optimal Admissible Strategies and Numerical Simulations. -
Abstract
This article explores the application of Forward-Backward Stochastic Differential Equations (FBSDEs) to cash flow optimization in uncertain financial environments. FBSDE provide a rigorous framework for modeling investment and payment dynamics, enabling the maximization of investor preferences while minimizing financial risks. The model considers a portfolio composed of both risky and risk-free assets, incorporating constraints such as the balance between discounted payments and accumulated premiums.
The analysis includes solving the optimization problem using the stochastic maximum principle and Lagrange multipliers. Optimal admissible strategies are defined as stochastic processes satisfying integrability conditions and backward differential equations. Numerical simulations assess the impact of key parameters, such as initial wealth, discount rate, volatility, and risk aversion, on investment and consumption decisions.
The results demonstrate that the FBSDE approach effectively captures complex dynamics and facilitates the development of robust strategies under uncertainty. In conclusion, this article highlights the potential of FBSDEs for portfolio management, financial product pricing, and decision optimization in uncertain environments. Future research could expand this framework by integrating exogenous factors, such as macroeconomic conditions, thereby broadening its applicability and relevance.
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How to Cite
T. Kayembe, T., K. Mubenga , P. ., K. Nawej , E. ., T. Tshisuaka, E. . ., & M. Mbuyi , E. . (2025). Cash flow optimization in uncertain environments: forward backward stochastic differential equation approach with pontryagin’s maximum principle. International Journal of Applied Mathematical Research, 14(1), 1-12. https://doi.org/10.14419/2frsms38