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**Minimum rate of return guarantees: the Danish case.**
*(English)*
Zbl 1039.91040

The authors deal with contracts where the customer receives a specified annual minimum rate of return, some of the bonus reserve during the life of the contract, and the amount on the bonus reserve (if positive) at maturity \(T\). If the bonus reserve is negative at date \(T\), then the company covers the deficit. This means that the company has issued a series of options on the annual returns. The authors work with three accounts on the liability side of the balance sheet: the customer account, the bonus reserve, and the company account. On the asset side we have the value of the customer investment which the company administers. The authors consider two different methods that the company can use to collect payment for the issuing minimum rate of return guarantee contracts: the direct method where the company gets a fixed fee of the customer saving each year, and the indirect method where the company gets a share of the distributed surplus. First, the one-customer case is considered and fair contracts between the customer and the company is characterized. In this case the customer will always have an initial bonus reserve of zero when he enters. At the maturity of the contract the customer will receive the remaining undistributed surplus. Second, the case with two customers is investigated. Two customers can differ with respect to the minimum rate of return guarantees, entry dates, and exit dates. The authors propose different mechanisms for distributing the final bonus between the customers depending on how the customers differ.

Reviewer: A. D. Borisenko (Kyïv)

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

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\textit{M. Hansen} and \textit{K. R. Miltersen}, Scand. Actuar. J. 2002, No. 4, 280--318 (2002; Zbl 1039.91040)

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