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The aim of this paper is to solve an optimal investment, consumption and lifeinsurance problem when the investor is restricted to capital guarantee. Weconsider an incomplete market described by a jump-diffusion model withstochastic volatility. Using the martingale approach, we prove the existence ofthe optimal strategy and the optimal martingale measure and we obtain theexplicit solutions for the power utility functions.

Optimal investment-consumption and life insurance with capital constraints