Markov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension

Abstract

We calculate reserves regarding expected policy holder behavior. The behavior is modeled to occur incidentally similarly to insurance risk. The focus is on multi-state modeling of insurance risk, e.g. in a disability model, and of behavioral risk, e.g. in a premium payment — free policy — surrender model. We discuss valuation techniques in the cases where the behavior is modeled to occur independently of insurance risk and where we take explicitly into account that e.g. disabled do not hold behavioral options, 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 in two contracts. For a "new" contract, i.e. low technical interest rate relative to the market interest rate, we obtain the lowest reserve by working with the correct model without inaccurate shortcut assumptions. For an "old" contract, i.e. high technical interest rate relative to the market interest rate, the picture is more blurred, depending on assumptions on reactivation (recovery) and the route of the shortcut.

Keywords: surrender option, free policy option, ordinary differential eqaution, recovery, dependence

JEL Classification: G22, G23, I12