Abstract
In many countries, the decline in interest rates has reduced the interest in traditional participating life insurance contracts with investment guarantees and has led to a shift to unit-linked policies without guarantees. We design a novel mixed insurance contract splitting premium payments between a participating and a unit-linked fund. An additional guarantee fee is applied on the unit-linked return in order to increase the investment guarantee of the participating fund. In a utility-based framework, using power utility and prospect theory as preference functions, we show that the mixed product is usually perceived more attractive than a full investment in either the unit-linked or the participating contract. The guarantee fee is beneficial for conservative investors interested in stronger protection against losses. This is also interesting from a marketing perspective: By the increase of the guarantee in the participating product, zero or negative guaranteed rates can be avoided.
Highlights
In many countries, the industry of life insurance has traditionally focused on products with guarantees
We describe an alternative behavioral model proposed by Tversky & Kahnemann (1992) called the cumulative prospect theory (CPT) that describes the human behaviors under risk and uncertainty
The product is not just a superposition of participating and unit-linked contracts but includes a continuous fee on the unit-linked part that permits a transfer from the unit-linked part to the participating part
Summary
The industry of life insurance has traditionally focused on products with guarantees. The typical example is given by participating life insurance contracts (or life insurance with profit), where the insurer offers ex ante a return guarantee and afterwards provides the client a participation in case the actual return exceeds this return guarantee These participation schemes may have different forms such as reversionary bonus or terminal bonus (Bacinello (2001); Bohnert & Gatzert (2011); Hieber, Natolski & Werner (2019)). The premiums are usually invested in the general fund of the insurer with no possible financial decision from the policyholder In parallel to this activity, new forms of life insurance products have emerged for decades in many markets under the form of unitlinked contracts or equity-linked contracts.
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