Abstract
We consider an optimal investment, consumption, and life insurance purchase problem for a wage earner. We treat a stochastic factor model that the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case that the wage earner can not observe the factor process and use only past information of risky assets. Then, our problem is formulated as a stochastic control problem with partial information. Applying the dynamic programming principle, we derive a coupled system of the Hamilton–Jacobi–Bellman (HJB) equation and two backward stochastic differential equations (BSDEs), and obtain the explicit solution. Finally, we strictly prove the verification theorem, and construct the optimal investment-consumption-insurance strategy.
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