Standard approaches to asset & liability risk**

Abstract

We compare two different models for assets and liabilities for an insurance company that can be considered in the standard approach to solvency assessment and in particular, in determining the required target capital. The first model is suggested by a joint working party by members in CEA, Comité Européen des Assurances, and is based on the duration concept and the second one is an application of ideas by Samuelson and Vasicek.

Keywords:

• solvency
• target capital
• asset liability
• coherent risk measure
• Value-at-Risk
• mismatch

The authors would like to thank Christer Borell and Sture Holm, Chalmers University of Technology, Arne Sandström, Swedish Insurance Federation, and Christer Stolt, Länsförsäkringar, for valuable discussions and support.

Notes

**Supported by the Swedish Insurance Federation.

¹Rantala actually uses Value at Risk. However, after some approximations he obtains a risk measure identical with the Standard Deviation Principle.

²Rantala has a plus sign instead of a minus sign, i.e. instead of . However, our formulation is closer to Macauley's formulation.

³Actually, Brown defines the duration based on the instantaneous spot rate instead of the “flat” interest rate