## Actuarial Science Seminar: Optimal Lifecycle Portfolio Choice with Natural Tontines under Systematic Longevity Risk

**Irina Gemmo, ETH Zurich**

### Friday 22 November 2019 (14h00 - 15h00) - Extranef - 126

The notion of stationarity has more a mathematical origin than a tight relationship to real data sets. Namely the underlying idea of this assumption is the use of the ergodic theorem (the law of large numbers). The aim of the talk is to try to provide mathematical models adapted to several issues of real data. We aim also at precisely setting some technical ideas for fitting such models. We will describe some models for astronomical data sets, for actuarial models for lifetables, in order to exhibit precise features of interest for real models, and we will try to avoid the standard mathematical traps to pass from stationary models to non stationary ones. Namely local stationarity, periods, exogenous data and isotonic assumptions are clearly seen to be reasonable. Weak dependence conditions are also quite valuable in such settings. We derive the optimal life-cycle portfolio choice and consumption pattern for a CRRA utility maximizing investor, facing risky capital market returns, systematic mortality risk and a stochastic level of living standard. In addition to stocks and bonds, the individuals have access to tontines. Tontines are cost-efficient financial contracts providing age-increasing, but volatile cash flows, generated through the pooling of mortality without guarantees, which can help to match increasing financing needs at old ages. We show that tontines can generate significant welfare gains. We find a decreasing optimal stake in tontines over the lifecycle to smooth consumption. Higher risk aversion reduces tontine investments and increases stock investment. Depending on the level of bequest motive, the tontine is crowded out by bequeathable assets. Furthermore, we find that the value of the tontine increases in the tontine size and risk aversion. However, since stochastic mortality affects both, expected tontine returns as well as tontine payout uncertainty, the welfare gains diminish.

**Published 8 October 2019**

HEC-DSA