Description: This paper proposes the use of stochastic compartment model methods for estimating both the current direct and current indirect costs of specific cancers and for forecasting future direct and indirect costs. From Transactions of Society of Actuaries 1982, Vol. 34.

Description: This session covers stochastic modeling processes currently in use and explores others that may be beneficial to health actuaries. From the Record of the Society of Actuaries, Vol. 31, No. 2, Session 76

Description: Random sum models with compound distributions are used extensively in modeling of insurance risks. Unfortunately, the compound distributions themselves are awkward to evaluate. Consequently, various numerical and analytical approximative techniques have been used. In this talk we derive various upper and lower bounds on the tails of compound distributions. Some notions in reliability theory are used.

Description: In computing actuarial measurements, such as the moments of present value functions for insurance and annuities, the stochastic nature of the interest rate is commonly ignored. This paper treats the interest rate as a normal random variable and presents general formulas for the mean and variance of the present value function for insurance and annuities. An example demonstrating these formulas is presented. It is found that taking the force of interest to be fixed at a mean value results in slightly underestimating the actuarial present value along with the variance for both insurance and annuities.

Description: Discussion of the movement toward principle-based reserves for LTC insurance.

Description: This paper introduces a new direction for evaluating numerically survival probabilities pointed out by H. Seal in his book ‘Survival Probabilities: The goal of Risk Theory’. Some of special cases can be considered as a weighted Poisson process with an infinitely divisible mixing distribution. This property is well known for the negative binomial case [gamma mixing distribution].

Description: In this paper, we derive three important longevity Greeks on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility.

Description: The research investigates the challenges associated with determining a “fair value” assessment for embedded options in two product types and incorporates the process into product pricing and liability valuation

Description: Discussion that developing credibility factors for group health insurance can be accomplished empirically through the use of stochastic models with appropriate parameters and fairly readily obtainable data, without the need for unrealistic assumptions.

Description: This paper illustrates the application of stochastic control methods in managing the risk associated with an insurance business. We present the Hamilton-Jacobi-Bellman HJB equation and demonstrate its use in finding the optimal investment strategy based on some given criteria. Here we consider an insurance business with a fixed amount available for investment in a portfolio consisting of one non-risky asset and one risky asset. The object of the resulting control problem is to determine the investment strategy that minimizes infinite time ruin probability. The existence of a solution to the resulting HJB equation is shown. The relevant verification lemma is not presented in this paper and a numerical algorithm is given instead. Examples applied to exponential claims are also presented.