A hybrid approach for solving the Merton portfolio optimization problem with an infinite horizon

Subject Areas : Mathematical Methods in Financial, Physical, Biological, Social, and Behavioral Sciences.

Mohammad Soleimanivareki ^{1 *} , mohammad soleimanivareki ² , Seyyed Ali Nabavi Chashmi ³

1 - Sa,C., Islamic Azad University, Sari, Mazandaran, Iran
2 - Department of Managemnet, Ba.C., Islamic Azad University, Babol, Iran.
3 - Department of Financial Management, Babol Branch, Islamic Azad University, Babol, Iran

Received: 2024-12-16 Accepted : 2025-10-15 Published : 2024-08-04

Keywords: Stochastic optimal control problems, Dynamic programming, Hamilton-Jacobi-Bellman equation, Merton’s Portfolio Problem,

Abstract :

In a world dominated by uncertainty, stochastic modeling is of the utmost importance, so that Many problems in economics, finance, and actuarial science naturally require decision makers to undertake choices in stochastic environments. Classical methods for solving infinite horizon stochastic optimal control problems primarily focus on deriving the solution by defining the value function through dynamic programming and the Hamilton-Jacobi-Bellman equation. However, obtaining a closed-form solution is generally challenging. To address this issue and identify an optimal trajectory and control, this article proposes a hybrid method for solving stochastic optimal control problems (SOCPs). This novel approach integrates the multi-step stochastic differential transform method with an approximation technique that solves infinite horizon problems by leveraging a finite horizon. An applicable example diagrams of the types of instances created from the simulation of the described approach, infinite horizon stochastic optimal control problem from management science is provided to show the method's effectiveness and efficiency, particularly in comparison with existing approaches.

 

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