Description: The main objective of this study is to analyze and control a surplus dependent risk process, where larger surpluses allow for a wider underwriting policy. We focus here mostly on the diffusion approximation of the risk process. The results are derived in two papers Brownian motion in Risk Theory, submitted for publication, and Surplus dependent risk processes defined by stochastic differential equations, in preparation. We only include here a long summary of these papers.

Description: In this paper we discuss some properties of the nth stop-loss order and their application in risk premium principles. We give a necessary condition and a sufficient condition for nth stop-loss orders. They are convenient tools to construct risk pairs with nth stop-loss orders. We show that exponential premium principles can diferentiate between losses more finely than the net premium principles under some conditions.

Description: This paper discusses a problem in corporate finance, the problem of selecting from among a group of possible economic projects. This problem most certainly involves future contingent events and is a natural for consideration by actuaries interested in expanding into non-traditional practice areas.

Description: In this note, the asymptotic behavior of the probability of ruin is derived by means of infinitesimal generators and Laplace transforms. Using these same tools, it is shown that the probability of ruin has an algebraic decay rate if the insurance company invests its capital in a risky asset with a price which follows a geometric Brownian motion. The latter result is shown to be valid not only for exponentially distributed claim amounts, as in Frolova et al. 2002, but, more generally, for any claim amount distribution that has a moment generating function defined in a neighborhood of the origin.

Description: This paper discusses a general model for calculating life contingencies including formulation of the model and net reserves and contingency reserves.

Description: In this paper, we introduce a political risk variable, d, to measure risk of foreign direct investment FDI. The political risk variable has opposite effects of loss reduction and loss prevention in Ehrlich and Becker 1972. The unique characteristics of political risk insurance make the applications of actuarially-based pricing models infeasible. In this study, by taking into account the effects of self-protection and self-insurance through the variable d and by maximizing utility function, we find the equilibrium for insured and insurer in a competitive market and in a monopoly one. In addition, under the equilibrium status, the boundary for the amount of investment, the insurance coverage, and the minimum required rate of return on the FDI are derived.

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: Non-consequentiality is quite consequential for the claims made for the applicability of Risk Theory RT to decision problems that are not transparently tactical or wholly instrumental. On the negative side, RT is not normative or even a complete heuristic in such contexts. The author takes strong exception to the common tendencies, A to link risk theory with welfarism and versions of utilitarianism, and B to claim that with or without but especially with such linkage RT is normative in both moral and rational analysis, choice and action.

Description: This paper demonstrates that the variance of the loss function for n-year term is greater than the sum of the variances of the loss functions for n-year pure endowment and n-year regular endowment plans. The result is true for both single premiums and annual premium plans.

Description: In the context of insurance economics, the PH-transform is justified through some basic postulates on market premiums. In this paper the PH-transform is applied to the present value random variable in life insurance and annuities. It provides an alternative to the commonly used equivalence principle in life insurance and annuities premium calculation. This research project is sponsored by a joint AERF/CKER Grant of the Society of Actuaries.