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Summary
In this chapter we introduce the concept of a policy value for a life insurance policy. Policy values are a fundamental tool in insurance risk management since they are used to determine the economic or regulatory capital needed to remain solvent, and are also used to determine the profit or loss for the company over any time period.
We start by considering the case where all cash flows take place at the start or end of a year. We define the policy value and we show how to calculate it recursively from year to year. We also show how to calculate the profit from a policy in any year and we introduce the asset share for a policy. Later in the chapter we consider policies where the cash flows are continuous and we derive Thiele's differential equation for policy values – the continuous time equivalent of the recursions for policies with annual cash flows. We also consider policy alterations.
Assumptions
In almost all the examples in this chapter we assume the Standard Select Survival Model specified in Example 3.13 on page 65 and used throughout Chapter 6. We assume, generally, that lives are select at the time they purchase their policies.
The default rate of interest is 5% per year, though different rates are used in some examples.
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