Reserves and cash flows under stochastic retirement

Specialeforsvar ved Thomas Nielsen

Titel: Reserves and cash flows under stochastic retirement

Abstract: The new solvency and accounting rules (Solvency II and IFRS) require that expected policyholder behaviour is taken into account and that the expected policyholder behaviour is supposed to take into account both the economic conditions under which the behaviour takes place as well as the extent to which intervention is to the benefit of the policyholder. The motivation in the first part of the thesis is to look at a Markov chain that is different from the one we normally look at. We will introduce a setup where we have point probabilities and derive an extended Kolmogorov backward integral equation and an extended Thieles differential equations. In real life these equations can help with the policyholder option that is the time of retirement. This is first done under the assumption we have deterministic intensities but where we let retirement happen with an intensity that also have positive probability at predefined time points. It is first done in a simple life-death model with a retirement state added and with a little more complexity with the free policy added. Another approach to modelling the intensity will be to let the intensity depend on internal factors relevant to the specific policy. We let it depend on the reserve itself. Here we place ourself in-between the purely random and the completely rational. The tendency to retire will depend on the gain from doing so 

Vejleder: Jesper Lund Pedersen
Censor:   Jesper Olesen, Danica Pension