Abstract
The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation of simple integrals. In the second part, a more general disability model with recovery is studied. Here, cash flows are determined by solving a modified Kolmogorov forward differential equation. We conclude the paper with numerical examples illustrating the methods proposed and the impact of policyholder behavior.
Highlights
We study policyholder behavior in life and pension insurance with a focus on two so-called policyholder options: first, the surrender option, where the policyholder may surrender the contract, canceling all future payments and instead receiving a single payment corresponding to the value of the contract on a technical basis; second, the free policy option1, where the policyholder may cancel the future premiums and have the benefits reduced according to the technical basis
In a classic Markov chain multi-state life insurance setup, we show how policyholder behavior can be included in cash flow projections
We show that the cash flows with policyholder behavior can be derived from cash flows with surrender behavior
Summary
We study policyholder behavior in life and pension insurance with a focus on two so-called policyholder options: first, the surrender option, where the policyholder may surrender the contract, canceling all future payments and instead receiving a single payment corresponding to the value of the contract on a technical basis; second, the free policy option , where the policyholder may cancel the future premiums and have the benefits reduced according to the technical basis. We extend the model by including first surrender behavior and both surrender and free policy behavior We see that these extensions can be obtained via simple modifications of the cash flows without policyholder behavior. We consider the more correct way of modeling policyholder behavior in a multi-state life insurance setup This model is presented in [1] for the general semi-Markov setup, and here, we present the special case of a Markov process for the disability model with recovery. We compare the approximate method with the correct approach of solving the modified Kolmogorov differential equations and find cash flows with policyholder behavior in a disability model. The proofs are more direct and should be easy to follow for readers familiar with the classic Markov models as presented in, e.g., [10]
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