Abstract
The paper is concerned with sustainable retirement spending towards the end of the human life cycle, which is a substantial quantitative problem in the pension framework. In [7] the authors successfully use an Arithmetic Asian option pricing concept to estimate an individual's probability of retirement ruin under constant spending rates and asset prices driven by the geometric Brownian motion.
Their model coherently links the three key factors of retirement planning: uncertain length of human life, uncertain investment returns and spending rates. The authors conclude that for an individual with a given investment portfolio, the expected rate of return and volatility of which are known, the probability of retirement ruin can be estimated using the reciprocal gamma distribution.
Building on the model described in [7], we extend the theoretical result to the case, when remaining length of human life follows the Gompertz-Makeham law of mortality. The accuracy of presented approximation is analysed via Monte Carlo simulations.
A numerical case study using Czech data is provided, including calculated maximal sustainable spending rates for Czech retirees under various combinations of wealth-to-spending ratios and investment portfolio characteristics. We also present optimal investment strategies for retirees with various risk of ruin tolerances.