Market consistent cash flows for benefits, tax and future profits in life and pension insurance

Speaker(s): Thomas Møller (PFA Pension)

We study the problem of valuating life insurance contracts in the presence of taxes and future profits. The basic framework consists of the classical finite state Markov chain model describing the possible states of the policy-holder and a stochastic model for the financial market. One approach to model the liabilities is to introduce a full simulation model for the relevant states of the policy holder and the payments associated with the contracts. We discuss how one can alternatively adopt analytical methods such as Thiele's differential equation for the state wise reserves and Kolmogorov's forward equations for the transition probabilities for determining the market values of  the various cash flows arising from the contracts. More precisely, we determine the tax cash flows for guaranteed and unguaranteed payments, tax payments and future profits for the owners. We also discuss how the market values of the cash flows can be determined without explicitly deriving the underlying cash flows. The cash flows for unguaranteed payments, taxes and profits will typically depend on the term structure, which is uncertain. We refer to these cash flows as term structure dependent cash flows.