Projection of Unit-Linked Policies, Monce Carlo methods for calculating expected future cashflows in life insurance

Specialeforsvar ved Martin Steen Andersen

Titel: Projection of Unit-Linked Policies Monte Carlo methods for calculating expected future cashflows in life insurance

Abstract: In this thesis the problem of calculating future expected cashflows for unit-linked life insurance contracts with policyholder behaviour modelling is studied. Firstly, in a simple survival model the cashflows are derived assuming constant interest rates. The cashflow is then calculated in the 7-state model. The calculation of these cashflow require us only to solve simple integrals. Secondly, we turn to unit-linked contracts and present Monte Carlo methods for calculating expected future cashflows. Here, the free policy modelling becomes particularly difficult. The difficulty arises from the complexity of calculating free policy fractions. As a result, we present new methods of calculating these cashflows without using the free policy fraction. We provide simple integrals satisfying simple ODE's similar to those presented in the traditional method. We also provide the free policy fractions whenever the product design is particularly simple, should they be needed. Assuming a Black-Scholes model, we derive closed form solutions for the expectations to which the averaged stochastic parts of the cashflow converge in the Monte Simulations. This eliminates the need to simulate in the Black-Scholes model. We study the convergence of the mean cashflows toward the derived expected values in a numerical example, and we assert that the free policy fractions provided for the traditional calculation method are correct. During the thesis we briefly comment on other subjects of interest. For example Economic Scenario Generated simulated cashflows and profit margin. We do not go in depth with these subjects, but present ideas on possible calculation techniques. Keywords: Cashflows, Monte Carlo Methods, Policyholder behaviour, Free policy option, Free policy fraction, Unit-link, Black-Scholes model, Economic Scenario Generation.

Vejleder:  Mogens Steffensen
Censor:   Jesper Olesen, Danica Pension