MINIMIZING BANKRUPTCY PROBABILITY OF A LIFE INSURER SOME ANALYTICAL CONSIDERATIONS

This paper studies the portfolio problem faced by a life insurance company which sells an annuity, collects fees/premiums for it as a lump-sum, and for solvency considerations invests in a financial market with several investment opportunities. The company has to choose the investment strategy (a portfolio) which minimizes the probability of being unable to pay the annuity before it stops being in force, and this occurs when portfolio value adjusted for annuity present value becomes negative. We manage to solve this stochastic control problem in closed form for constant mortality intensity, and we found out that the optimal investment in stock is decreasing in initial wealth. Moreover if the initial wealth exceeds a threshold the optimal investment in stock is decreasing in mortality intensity. The stochastic mortality intensity case is more involved and we perform duality techniques and asymptotic expansions to tackle it, and established the following qualitative result: in a model with stochastic intensity the probability of company default is higher than in a model with constant intensity fact explained by the extra source of risk (longevity risk) faced by the insurance company.