Comonotonic approximations for the probability of lifetime ruin

Abstract

This paper addresses the issue of lifetime ruin, which is defined as running out of money before death. Taking into account the random nature of the remaining lifetime, we discuss how a retiree should invest in order to avoid lifetime ruin. We also discuss the conditional time of lifetime ruin and the notion of bequest or wealth at death.Using analytical approximations based on comonotonicity, we provide a new approach which is easy to understand and leads to very accurate results without computationally complex calculations. Our analytical approach avoids simulation, which allows to solve very general optimal portfolio selection problems.

Long-Run Savings and Investment Strategy Optimization

“…The probability of a lifetime ruin is already studied by [14], as well as optimal portfolio selection terminal wealth problems (see [15]). Lifetime ruin has received increased attention (see, [16]).…”

“…Our focus here is the expected shortfall risk measures [ 7 , 8 ] such as downside value at risk [ 9 , 10 ] and tail conditional expectation [ 11 – 13 ] which are widely accepted in financial economics. The probability of a lifetime ruin is already studied by [ 14 ], as well as optimal portfolio selection terminal wealth problems (see [ 15 ]). Lifetime ruin has received increased attention (see, [ 16 ]).…”