Description: It is assumed that the force of interest varies as an auto-regressive process of order 2, AR[2]. The moments of the accumulated value of 1 paid at the beginning of each period, for n periods, are developed using moment generating functions.

Description: Annual reports of the U.S. Social Security Trustees present 75-year financial projections of the system under three different deterministic sets of economic and demographic assumptions or scenarios. The extent of the divergence between these scenarios provides useful information concerning the range of possible outcomes, but, in the absence of stochastic model projections, no probability measure can be assigned to the three scenarios, apart from being described as intermediate, low-cost and high-cost. Demographic research and stochastic model forecasts of U.S. population suggest plausible hypotheses for analysis of the divergence characteristics of the actuarial solvency ratios implied by the three deterministic scenarios. Available data from the 2002 Trustees’ report are presented and various statistical measures are developed to aid in the assessment of plausible associated probability measures for the scenario projections.

Description: This paper represents a brief progress report on research, being sponsored by the Casualty Actuarial Society and the Society of Actuaries, in the area of modeling of economic series. In particular, research is being undertaken to provide a foundation for the actuarial community’s modeling of a variety of economic variables, including interest rates, equity returns, inflation, unemployment rates, and real estate price levels. The specific objectives of this research are to provide a summary of the literature in the area of economic scenario modeling, identify data sources and methodologies in this area useful to the actuarial profession, and produce working software for economic modeling, including appropriate documentation, to be made available to the general actuarial community in order to allow actuaries to use and build upon this research. From Actuarial Research Clearing House 2004, Vol. 1.

Description: With this paper, a new theory of immunization is introduced in which the approach is multivariate, and the goal is stochastic in the sense of minimizing stochastic risk. Discussions of this paper are included.

Description: A classical risk model with a multi-layer premium rate is considered in this paper. In the two-layer case, an explicit expression is obtained for the joint distribution of the maximal surplus up to ruin, the surplus immediately before ruin and the deficit at ruin. Such an expression involves some known results on the joint distribution at ruin for a risk model with a constant premium rate. In the multi-layer case, a scheme is proposed to compute its ruin probability.

Description: This session of the SOA 2003 Washington, DC Spring Meeting covers the basics of stochastic modeling with focus on random number and scenario generation, steps in creating models, and verification of models and assumptions.