Elimination of Path Dependencies for Projection of Cash FLows in Multi-State Life Insurance

Specialeforsvar ved Jamaal Ahmad

Titel: Elimination of Path Dependencies for Projection of Cash Flows in Multi-State Life Insurance

Abstract:
In participating life insurance, the complexity of the underlying payments is high. This challenges classic analytical methods to valuate liabilities, and thus one may use simulation methods to project cash flows into future time points. In this thesis, we present an efficient simulation method that eliminates path dependencies in biometric states, such that only financial scenarios needs to be simulated. This is studied in the classic multi-state Markov setup with stochastic interest rates, surplus- and bonus-linked dividends and additional benefits. Our main result is an explicit system of ordinary differential equations to project bonus allocations and surplus in each financial scenario under the assumption of dividends being affine in bonus and surplus. This allows us to project cash flows that includes future additional benefits, and in particular, to  calculate the bonus potential today by discounting bonus cash flows. We further examine performance optimizations by approximating projections of bonus in two different ways. This allows us to use market value cash flows calculated today in the projections. In a numerical study, one of these is seen to perform well when dividends can be assumed to be allocated on portfolio level. Lastly, we extend our general multi-state Markov setup to include the surrender and free policy option. We demonstrate that we are able to project cash flows using the same methods as in the original setup, and, under the assumption of not buying additional benefits after free policy conversion, we show that bonus cash flows are calculated by extending methods from the original setup with a Q-modified system of Kolmogorov’s forward differential equations needed to be solved in each scenario.

Vejledere: Mogens Steffensen, Christian Furrer

Medvejleder: Kristian Buchardt, PFA Pension

Censor:     Ninna Reitzel Heegaard, ATP