Ph.D.-forsvar ved Kamille Tågholt Gad

PhD defence by Kamille Tågholt Gad.

Optimal Stopping and Policyholder Behaviour in Life Insurance.

Abstract: 
The topics of thesis are all centered around stopping times, but they may be separated into two parts. In the first part we solve two non-linear optimal stopping problems with geometric Lévy processes as the underlying process. The first problem concerns maximizing variance and the second maximizing expectation minus a constant times the variance. For both problems we find that randomized stopping times play an important role. This is in contrast with what is known for similar problems based on geometric Brownian motions.

In the second part we model behaviour of holders of financials options. When and agent faces the choice of exercising an option at a time of his own choice, stopping times may formalize which strategies the agent can possibly follow. We first discuss modelling of exercise of an American put and exercise of a surrender option for a life insurance contract. For both options we suggest the exercise of the option depends on the profitability of exercising. We give a probabilistic proof of the intuitive result that when the dependence on profitability increases suitably, the value of the contract converges to the value corresponding to the holder of the option exercising optimally. At last we study modelling of the time of retirement. The time of retirement and the structure of retirement benefits have traditionally been modelled as deterministic. We suggest to model these as stochastic and present how to scale benefits, and how to calculate market reserves and expected cash flows.

Supervisor: Jesper Lund Pedersen, University of Copenhagen
Co-supervisor: Mogens Steensen, University of Copenhagen