Hamilton-Jacobi-Bellman Equation Arising from Optimal Portfolio Selection Problem

TL;DR

This paper investigates the Hamilton-Jacobi-Bellman equation from optimal portfolio selection using advanced mathematical methods to establish existence and uniqueness of solutions in an abstract framework.

Contribution

It introduces a novel application of maximal monotone operator methods to analyze the HJB equation in portfolio optimization.

Findings

Proves existence of solutions using Banach fixed-point theorem.

Establishes uniqueness of solutions via monotone operator techniques.

Provides a rigorous mathematical framework for the HJB equation in finance.

Abstract

The Hamilton-Jacobi-Bellman equation arising from the optimal portfolio selection problem is studied by means of the maximal monotone operator method. The existence and uniqueness of a solution to the Cauchy problem for the nonlinear parabolic partial integral differential equation in an abstract setting are investigated by using the Banach fixed-point theorem, the Fourier transform, and the monotone operators technique.