Sustainable retirement spending: the Czech case

Abstract

The paper is concerned with retirement planning, in particular with sustainable retirement spending towards the end of the human life cycle, which is a substantial quantitative problem in the pension framework. Some authors have recently successfully used 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. It was concluded 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. We extend this 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.