Optimal investment-consumption and life insurance with capital constraints

TL;DR

This paper addresses an optimal investment, consumption, and life insurance problem under capital constraints in an incomplete jump-diffusion market with stochastic volatility, providing explicit solutions for power utility functions.

Contribution

It introduces a martingale approach to solve the constrained problem and derives explicit solutions in a complex market setting.

Findings

Existence of optimal strategies proven

Explicit solutions obtained for power utility functions

Applicable to markets with jumps and stochastic volatility

Abstract

The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal strategy and the optimal martingale measure and we obtain the explicit solutions for the power utility functions.