Robust retirement and life insurance with inflation risk and model ambiguity

We study a robust consumption-investment problem with retirement and life insurance decisions for an agent who is concerned about inflation risk and model ambiguity. Assuming that an inflation-linked index bond and a stock are available in the market, this paper considers a comprehensive setup of ambiguity in the return, volatility, and correlation parameters in the joint dynamics of their market prices. With a finite planning horizon, the agent has a general utility function with different marginal utilities of consumption before and after retirement. Combining the classical dual approach and the G-stopping time theory, we derive the novel robust strategies using integral equation representations. We numerically and extensively investigate the effects of ambiguity from different sources on the robust decisions. While model ambiguity generally leads the ambiguity- and risk-averse agent to decrease the consumption rate, life insurance purchase, and investment demands, it also generates contrasting effects on robust retirement time and wealth level. Specifically, model ambiguity lowers the target wealth level to immediate retirement of a young agent but increases the retirement time of an older agent compared to the case of known parameters. A rich agent takes ambiguity more seriously than a poor agent in the sense of adjusting the strategies on a more significant scale. Our simulation and comparison study demonstrate the significance of addressing the ambiguity in volatility and correlation in addition to the ambiguity in return.