Optimal Consumption and Investment with Insurer Default Risk

We solve the optimal consumption and investment problem in an incomplete market, where borrowing constraints and insurer default risk are considered jointly. We derive in closed-form the optimal consumption and investment strategies. We find two main results with quantitative analysis. On the one hand, the proportion of wealth invested in stocks could increase (decrease) as insurer default risk increases when wealth is low (high). On the other hand, the voluntary annuity demand could increase (decrease) as risk aversion increases when insurer default risk is small (large)