Optimal investment, consumption and life insurance problem with labour income and jump-diffusion model

Abstract Optimal investment, consumption and life insurance control problem with labour income and jump-diffusion model for a CRRA wage earner is solved in this study. The wage earner invest in thefinancial market with one bond, two stocks, receive labor income and has a life insurance policy resulting toan incomplete market. The two stocks are described by jump-diffusion processes. Investors are concernedwith sudden breaks or jumps in the dynamics of the risky securities. We investigates optimal investmentconsumption-insurance premium strategies that maximize the expected utility of consumption, legacy andterminal wealth under jump-diffusion models. A life insurance policy is purchased in order to hedge thefinancial wealth for the beneficiary in case of wage earner premature death. By applying Martingale approach,we prove the existence of optimal controls and optimal martingale measure