In this paper, we consider an optimal consumption and investment problem for a partially annuitized individual in the presence of the default risk of insurance company. We veri¯ed
the relationships between individuals optimal consumption and investment behaviors and the default risk of insurance company. Numerical results tell us that the existence of the default risk can give a signi¯cant e®ect on the optimal behaviors of such individual. Furthermore, using the numerical results we found that the individual who invests large portion of her wealth in annuities has a strong demand for selling or refunding her annuities when facing the default risk of insurance company, therefore we suggest an opinion for the annuity puzzle that individuals recognition of the default risk of insurance company may interrupt the growth of annuity markets.