گزینه مداخله در بیمه عمر

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.

The market reserve on an insurance contract is in Steffensen (2000b) defined as the market price of future contractual payments. We shall work with the same notion of the reserve, but since this is the only reserve present here we will suppress the word market and simply speak of the reserve. It is a difficult task to describe in detail the payments stipulated in an insurance contract including the various options that may be held by the policy holder, the insurance company, and the supervisory authorities. In several papers, published during the last decades, the authors bring some of these options to the surface and deal with their impact on the pricing and the reservation problems.

In this section, we consider a model where payments depend on the present state of X. Hoem (1969) obtained in this model a version of Thiele’s differential equation which has taken a central position in life insurance mathematics and is widely used by practitioners