This paper examines a class of premium functionals which are (i) comonotonic additive and (ii) stochastic dominance preservative. The representation for this class is a transformation of the decumulative distribution function. It has close connections with the recent developments in economic decision theory and non-additive measure theory. Among a few elementary members of this class, the proportional hazard transform seems to stand out as being most plausible for actuaries.

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In this paper, we investigate the notion of dependency between risks and its effect on the related stop-loss premiums. The concept of comonotonicity. being an extreme case of dependency, is discussed in detail. For the bivariate case, it is shown that, given the distributions of the individual risks, comonotonicity leads to maximal stop-loss premiums. Some properties of stop-loss order preserving premium principles are considered. A simple proof is given for the sub-additivity property of Wang's premium principle.

Normalized exponential tilting is an extension of classical theories, including the Capital Asset Pricing Model (CAPM) and the Black-Merton-Scholes model, to price risks with general-shaped distributions. The need for changing multivariate probability measures arises in pricing contingent claims on multiple underlying assets or liabilities. In this article, we apply it to valuation of mortality-based securities written on mortality indices of several countries. We show how to use multivariate exponential tilting to price the first pure mortality security, the Swiss Re bond. The same technique can be applied in other mortality securitization pricing. Copyright The Journal of Risk and Insurance, 2006.

Based on recurrence equation theory and relative error (rather than absolute error) analysis, the concept and criterion for the stability of a recurrence equation are clarified. A family of recursions, called congruent recursions, is proved to be strongly stable in evaluating its non-negative solutions. A type of strongly unstable recursion is identified. The recursive formula discussed by PANJER (1981) is proved to be strongly stable in evaluating the compound Poisson and the compound Negative Binomial (including Geometric) distributions. For the compound Binomial distribution, the recursion is shown to be unstable. A simple method to cope with this instability is proposed. Many other recursions are reviewed. Illustrative numerical examples are given.