Stochastic Retirement - a Non-Purely Incidental Approach

Specialeforsvar: Olivia Juul-Branth

Titel: Stochastic Retirement - a Non-Purely Incidental Approach

Abstract: This thesis is concerned with the modeling of retirement as policyholder behaviour rather than a deterministic event. Approaches to this are categorized into purely incidental and nonpurely incidental retirement, and both types of approaches are studied and compared. The mathematical framework is Markov modeling, but based on cumulative transition intensities as
an alternative to the usual transition intensities, which allows for the inclusion of point probability mass in the jump distributions. From this, methods to valuate life insurance contracts that include a policyholder option are derived. In particular, we resolve the circularity that arise from a reserve-dependent intensity, thus allowing for a non-purely incidental approach to
stochastic retirement. Lastly, the impact on the market valuation, when modeling with stochastic retirement, is examined. This is done by implementing two simple retirement models, one assuming purely incidental retirement and the other non-purely incidental retirement, where the numerical results are evaluated and compared.

Vejleder: Christian Furrer
Censor:    Lars Frederik Brandt Henriksen, PFA