Computational insights into optimal household portfolio decisions: a stochastic approach with heston model and finite difference scheme

This work develops and solves an intertemporal household portfolio problem to address the fundamentals of contemporary asset pricing theory. The model incorporates stochastic market volatility according to the Heston model and assumes constant wage income. The problem formulation makes use of sophisticated mathematical techniques, particularly stochastic calculus, and the stochastic control framework. The partial differential equation (PDE) is developed, and a finite difference scheme (FDS) combined with the Feynman–Kac theorem yields optimum controls. Python is used to build the numerical solution, which offers insights into the best portfolio selections for households dealing with erratic market situations. In the framework of stochastic market dynamics, this study advances our knowledge of portfolio decision problems by fusing computational methods with mathematical rigour to produce workable answers.