Multiperiod Insurance Supervision: Top-Down Models

19 Pages Posted: 11 Mar 2012  

Karl-Theodor Eisele

University of Strasbourg

Philippe Artzner

affiliation not provided to SSRN

Date Written: March 11, 2012


We describe a top-down procedure for the supervisory accounting of insurance companies with special emphasis on market impacts. The technical tools are a multiperiod risk assessment, a market consistent best estimate and an eligible asset. First, to avoid supervisory arbitrage by financial market instruments, the risk assessment is bounded by a market consistent best estimate. Applied to the risk bearing capital, i.e. asset value minus best estimate of obligations, the risk assessment immediately gives the free capital which has to be positive for acceptability. Next, optimal hedging of the obligation process by suitable asset portfolios yields the supervisory provision as the minimal initial value of a portfolio acceptable with respect to the given obligations. The problem to attain this minimal value leads to the definition of an optimal replicating portfolio. A further task of supervision is the determination of the 'Fremd'-capital in the supervisory balance sheet. This is formalized by the cost-of-capital method, i.e. a fictitious standardized transfer of the obligations to new investors on the market. The regulated price of such a transfer leads to the technical provision and the risk margin as 'Fremd' - capital items.

Finally, the additional financial risks within the insurance’s real asset portfolio are taken care of by the solvency capital requirement defined as the minimal acceptable ‘Eigen’ - capital for a given business plan. It measures the adequacy or inadequacy of the trading risks incorporated in the portfolio with respect to the obligation risks. An optimal replicating portfolio is characterized by a minimal solvency capital requirement. Solvency II and the Swiss Solvency Test (SST) are defined as bottom-up models. In the forthcoming paper Eisele and Artzner (2011), we shall show how bottom-up and top-down models can be made congruent.

Keywords: cost of capital, 'Fremd’'- versus ‘Eigen’ - capital (own funds), optimal replicating portfolio, regulated market, risk margin, solvency capital requirement, time consistency

JEL Classification: G28

Suggested Citation

Eisele, Karl-Theodor and Artzner, Philippe, Multiperiod Insurance Supervision: Top-Down Models (March 11, 2012). Available at SSRN: or

Karl-Theodor Eisele (Contact Author)

University of Strasbourg ( email )

Strasbourg, Alsace

Philippe Artzner

affiliation not provided to SSRN ( email )

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