A Generalized Finite Difference Method for Solving Hamilton–Jacobi–Bellman Equations in Optimal Investment

This paper studies the numerical algorithm of stochastic control problems in investment optimization. Investors choose optimal to maximize expected return under uncertainty. The optimality condition, Hamilton–Jacobi–Bellman (HJB) equation, satisfied by value function and obtained dynamic programming method, is a partial differential equation coupled with One major computational difficulties irregular boundary conditions presented HJB equation. In this paper, two mesh-free algorithms are proposed solve different cases equations regular conditions. model uncertainty developed Abel used study efficacy algorithms. Extensive conducted test impact key parameters on efficacy. By comparing solution exact solution, validated.