Stochastic Modellization of Hybrid Public Pension Plans (PAYG) under Demographic Risks with Application to the Belgian Case

Aging is an important challenge for pension schemes, especially for social security plans mainly 􏰂nanced by PAYG (Pay as you go) and based on a DB formula (De􏰂ned Bene􏰂t). In particular, demographic risks induce important increases of the contributions and threaten the 􏰂nancial sustainability of such schemes. On the other hand, switching to De􏰂ned Contribution plans can be a solution in terms of funding but introduce signi􏰂cant risks in terms of social adequacy. The purpose of this paper is to study hybrid solutions between DB and DC in a stochastic environment. In particular, we simulate for various risk sharing strategies, the evolution of contributions and bene􏰂ts by introducing risk factors in􏰃uencing the demographic dependence ratio (fertility, longevity, baby boom). We study the mean evolution of these processes as well as their value at risk.