A numerical method for annuity-purchasing decision making to minimize the probability of financial ruin for regime-switching wealth models

Abstract

This work develops an approximation procedure to find optimal annuity-purchasing strategies for minimizing the probability of lifetime ruin. The wealth is modelled as a regime-switching diffusion modulated by a continuous-time Markov chain. Based on Markov chain approximation techniques, a discrete-time controlled Markov chain with two components is constructed. Under simple conditions, the convergence of the approximation sequence to the wealth process is obtained. The convergence of the approximation to the value function is also established. Several examples are provided to demonstrate the performance of the algorithms.

Keywords:

• annuity
• lifetime ruin
• stochastic control
• variational inequality
• regime switching
• Markov chain approximation

2010 AMS Subject Classifications :

• 65C30
• 60H35
• 65C05
• 91B28
• 91B70

Acknowledgements

Research of Z. Jin was supported in part by the National Science Foundation under DMS-0603287. Research of G. Yin was supported in part by the National Science Foundation under DMS-0907753.