Willow Tree Approach to Optimal Investment with Capital Restriction under Merton’s Jump Diffusion Model

This article extends the willow tree method, which is originally developed for option pricing, combines it with the theory of dual control in a novel way, and develops a new general willow tree framework for solving optimal investment problems with discretionary stopping under the Merton jump diffusion model. It is not only efficient and accurate, but also flexible, allowing for general underlying stochastic processes and utility functions. Numerical examples demonstrate the superior performance of the proposed willow tree framework as compared to the literature.