Interest rate modelling in with-profit life insurance using linear dividend strategies

Specialeforsvar: Kasper Nørmark Hansen

Titel: Interest rate modelling in with-profit life insurance using linear dividend strategies

Abstract: With-profit life insurance represents the classic approach for valuing an insurance contract between a policyholder and a life insurance company. The contracts are structured such that a systematic surplus, dependent on a financial market, is generated. This needs to be returned to the policyholder in the form of bonus payments. In the first part of the thesis, a partial differential equation (PDE) characterizing the market reserve is derived. This is the expected present value of future guaranteed payments and future bonus payments in a model with stochastic interest rates. The dimension of the PDE is reduced in the case of linear dividends, and the implications on the value of the market reserve using two different choices of interest rate models
are studied through a numerical example. With the introduction of the Solvency II regulations, it is becoming increasingly more necessary to model the financial market and the policyholder behaviour as dependent processes. As a consequence of this, insurance companies need to find appropriate models for this dependence, particularly for the surrender option. In the second part of the thesis, we derive a PDE characterizing the market reserve with a stochastic interest rate and a stochastic surrender intensity, such that the interest rate and the stochastic surrender intensity are dependent, adhering to the Solvency II regulations. We reduce the dimension of the PDE under the assumption of linear withdrawal penalty and linear dividends, and the consequences of having either completely dependent or independent processes are discussed. The thesis concludes with a presentation of parameter estimation in the proposed models.

Vejledere: Mogens Steffensen
                    Alexander Sevel Lollike, Edlund

Censor: Kenneth Bruhn, Edlund