Markov chain modeling of policyholder behavior in life insurance and pension

Abstract

We calculate reserves regarding expected policyholder behavior. The behavior is modeled to occur incidentally similarly to insurance risk. The focus is on multi-state modelling of insurance risk and behavioral risk in terms of free policy risk and surrender risk. We discuss valuation techniques in the cases where behavior is modeled to occur independently or dependently of insurance risk, respectively. Ordinary differential equations make it easier to work with dependence between insurance risk and behavior risk. We analyze the effects of the underlying behavioral assumptions for two contracts. For a “new” contract with low technical interest rate relative to the market interest rate, we obtain the lowest reserve by counting in dependence. For an “old” contract with high technical interest rate relative to the market interest rate, the picture is more blurred, depending on assumptions on reactivation (recovery) and independence.