Capital Allocation Principle Research Articles

Use of an Internal Model in a General Insurance Company: Focus on Economic Capital Allocation

Capital allocation is an instrument for managing an insurance company. This is linked with three important fields of an insurance company: pricing, risk management and performance management. It is a tool for strategic management so as to decide to further invest in or discontinue a business line. The toolbox behind such an exercise contains coherent risk measures as well as coherent allocation principles. These constitutes the rigorous axiomatic part of the exercise, that may be relaxed for practical purposes. An application is proposed through an internal model approach, triggered by the frameworks of insurance current solvency regimes, namely United Kingdom (UK) Internal Capital Adequacy Standards (ICAS) and Solvency II. This application is dealing with the combination of Aumann-Shapley also known as Euler-gradient Capital allocation principles with VaR and TVaR.

Quantifying mortality risk in small defined-benefit pension schemes

A risk of small defined-benefit pension schemes is that there are too few members to eliminate idiosyncratic mortality risk, that is, there are too few members to effectively pool mortality risk. This means that when there are few members in the scheme, there is an increased risk of the liability value deviating significantly from the expected liability value, as compared to a large scheme. We quantify this risk through examining the coefficient of variation of a scheme's liability value relative to its expected value. We examine how the coefficient of variation varies with the number of members and find that, even with a few hundred members in the scheme, idiosyncratic mortality risk may still be significant. Next we quantify the amount of the mortality risk concentrated in the executive section of the scheme, where the executives receive a benefit that is higher than the non-executive benefit. We use the Euler capital allocation principle to allocate the total standard deviation of the liability value between the executive and non-executive sections. The results suggest that the mortality risk of the scheme should be monitored and managed within the sections of a scheme and not only on a scheme-wide basis.

Some results on the CTE-based capital allocation rule

Tasche [Tasche, D., 1999. Risk contributions and performance measurement. Working paper, Technische Universität München] introduces a capital allocation principle where the capital allocated to each risk unit can be expressed in terms of its contribution to the conditional tail expectation (CTE) of the aggregate risk. Panjer [Panjer, H.H., 2002. Measurement of risk, solvency requirements and allocation of capital within financial conglomerates. Institute of Insurance and Pension Research, University of Waterloo, Research Report 01–15] derives a closed-form expression for this allocation rule in the multivariate normal case. Landsman and Valdez [Landsman, Z., Valdez, E., 2002. Tail conditional expectations for elliptical distributions. North American Actuarial J. 7 (4)] generalize Panjer’s result to the class of multivariate elliptical distributions. In this paper we provide an alternative and simpler proof for the CTE-based allocation formula in the elliptical case. Furthermore, we derive accurate and easy computable closed-form approximations for this allocation formula for sums that involve normal and lognormal risks.

Some Results on the Cte Based Capital Allocation Rule

Tasche (1999) introduces a capital allocation principle where the capital allocated to each risk unit can be expressed in terms of its contribution to the conditional tail expectation (CTE) of the aggregate risk. Panjer (2002) derives a closed-form expression for this allocation rule in the multivariate normal case. Landsman & Valdez (2003) generalise Panjer's result to the class of multivariate elliptical distributions.In this paper we provide an alternative and simpler proof for the CTE based allocation formula in the elliptical case. Furthermore, we derive accurate and easy computable closed-form approximations for this allocation formula for sums that involve normal and lognormal risks.

Capital Allocation for Insurance Companies: Issues and Methods

We address some key issues related to risk and capital allocation in insurance companies. We argue that the Froot-Stein approach to risk is relevant to a number of important problems in the daily management of an insurance portfolio and that - taken to its consequence - this approach will lead to a close co-operation between actuarial and financial departments with a particular view to the actuaries ability to separate financial risk from insurance risk and the ability of the finance department to hedge the right amount of their complicated financial risk at a good price. Further, we introduce a new capital allocation principle based on the solvency of the entire company and we claim that this principle is more robust than traditional methods. We also introduce a new way of combining capital allocation and pricing of insurance policies. Through a performance measure of return on capital, we suggest a way of evaluating the price of capital for a single policy, that this money is held as a reserve and that this reserve should run off in such a way that old underwriting does not harm the performance of any given business line.