Application of maximal monotone operator method for solving Hamilton–Jacobi–Bellman equation arising from optimal portfolio selection problem

In this paper, we investigate a fully nonlinear evolutionary Hamilton–Jacobi–Bellman (HJB) parabolic equation utilizing the monotone operator technique. We consider HJB arising from portfolio optimization selection, where goal is to maximize conditional expected value of terminal utility portfolio. The transformed into quasilinear using so-called Riccati transformation method. can be viewed as porous media type with source term. Under some assumptions, obtain that diffusion function globally Lipschitz continuous, which crucial requirement for solving Cauchy problem. employ Banach’s fixed point theorem existence and uniqueness solution general form in suitable Sobolev space an abstract setting. Some financial applications proposed result are presented one-dimensional space.