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 addition to death and maturity guarantees on the mutual funds they sell, some insurance companies make it possible for the investor to extend the guarantees for a fixed number of years. In this paper, we consider the case when that option is of the European type that is, the investor, at maturity, can either close out the contract or extend it for the stated, fixed term. When extended, the guarantee is on the value of the fund at the original maturity date. The fund is assumed to be fully invested in common stock.

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

Description: This work describes a study undertaken to determine whether the Federal Housing Administration FHA should modify or discontinue its single-family home mortgage insurance program for investor i.e., non-occupant loans.

Description: The article provides a complete and rigorous analysis based on calculus for the topics in the theory of compound interest: the monotone convergence properties of the rates of interest and discount payable m times per interest conversion period in relation to the force of interest, the monotone convergence properties of the present value and accumulated value of an ordinary annuity with m payments per interest conversion period in relation to those of a continuously paying ordinary annuity and a method for approximating the present value of an ordinary annuity, or an increasing annuity with m payments per interest conversion period, by accumulating, at compound interest for the fraction m - l/2m of an interest conversion period, the present value of the same type of annuity with one payment per interest conversion period.

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.

Description: This paper builds a new risk model for a firm which is sensitive to its credit quality. A modified Jarrow, Lando and Turnball model [Markov Chain model] is used to model the credit rating. Recursive equations for finite time ruin probability and distribution of ruin time are derived. Coupled Volterra type integral equation systems for ultimate ruin probability, severity of ruin and joint distribution of surplus before and after ruin are also obtained. Some numerical results are included.

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.