Willow Algorithm for Consumption-Investment under Stochastic Volatility Model with Jump Diffusion

Abstract

We mainly focus on the willow algorithm which can be used to solve the optimal dynamic multi-cycle investment and consumption problem under the jump-diffusion stochastic volatility model. First we obtain the moment generating function of the risky asset and then coalescing the Johnson-Curve transformation theory to generate the willow algorithm, which solving the multi-cycle dynamic investment and consumption problem is designed based on the two-dimensional willow framework. Moreover, through comparing our proposed solution with the optimal investment and consumption display solutions under the geometric Brownian motion model, we further discuss the analysis of the willow algorithm sensitivity. The willow algorithm for optimal investment and consumption proposed in this paper is able to extend the willow method which is effective from the field of option pricing to the field of investment portfolio, and it also provides a new idea for numerically solving the multi-period optimal investment and consumption decision.