Description: Statistical properties of interest, annuity and insurance functions are examined when mortality and interest are treated as having a random component. Several special models of interest rate fluctuation are examined in detail. It is hoped that such theory will be useful in developing fluctuation reserves and premium margins. Presented at the 13th Annual Actuarial Research Conference, Ball State University, August 31st. September lst, 2nd. 1978.

Description: This paper addresses the allocation of solvency capital in multi- line financial businesses. Although this paper is uniformly applicable to financial enterprises of all types, the terminology in the paper is mainly that of insurance. The TailVaR risk measure is extended in a natural way to allocating capital to each of the business units. This method of allocation allocates capital in a way that is invariant over the method of decomposing the enterprise into business units. Analytic results are derived in the case of multivariate Normal risks. The key result of this paper is that the TailVaR-based proportional allocation of total required capital is identical to that based on mean-variance considerations analogous to the CAPM in the case of the multivariate Normaldistribution.