Intervention options in life insurance

We deal with the intervention options of the policy holder in life insurance. To these options belong the surrender and the free policy (paid-up policy) options. Our approach is to let payments be driven by processes in which the policy holder is allowed to intervene. The main result is a quasi-variational inequality describing the market reserve on an insurance contract taking into account intervention options. The quasi-variational inequality generalizes Thiele’s differential equation used for calculation of reserves on a policy without intervention options. It also generalizes the classical variational inequality used for calculation of the price of an American option.