Early default risk and surrender risk: impacts on participating life insurance policies. (English) Zbl 1398.91318
Summary: We study the risk-neutral valuation of participating life insurance policies with surrender guarantees when an early default mechanism, forcing an insurance company to be liquidated once a solvency threshold is reached, is imposed by a regulator. The early default regulation affects the policies’ value not only directly via changing the policies’ payment stream but also indirectly via influencing policyholder’s surrender. In this paper, we endogenize surrender risk by assuming a representative policyholder’s surrender intensity bounded from below and from above and uncover the impact of the regulation on the policyholder’s surrender decision making. A partial differential equation is derived to characterize the price of a participating policy and solved with the finite difference method. We discuss the impacts of the early default regulation and insurance company’s reaction to the regulation in terms of its investment strategy on the policyholder’s surrender as well as on the contract value, which depend on the policyholder’s rationality level.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
participating life insurance policies; regulator’s intervention; early default risk; surrender risk; partial rationality; pricing partial differential equationReferences:
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