Description: This is a summary of the presentation given during the ARC Conference. Its purpose was to give a brief introduction to subexponential behavior and to show that the family of subexponential distributions provides ideal characteristics to model insurance risks. Although the literature related to this topic accumulated quickly during the last years, a textbook explaining the applications of extreme value theory with intuition as well as insight was still to be written. Embrechts et al, {I 997} satisfies this need and most of the results presented here can be found in this new classic in the actuarial literature.

Description: Market consistent valuations require path-dependent discounting for scenarios. IFRS 17's requirement to discount best-estimate cashflows using locked-in rates could give non-sensical results in many instances. This article describes a technique for calibrating each of the scenario's cashflows so that they can be discounted with other discount factors or curves without distorting the value of underlying options and guarantees.

Description: This article describes the key elements of a review of an economic scenario generator (ESG), including scoping, parameters, models, and model efficiency.

Description: In this article the author cautions against the temptation to extend stochastic modeling into areas of unpredictable parameters and probabilities. He challenges actuaries to rely on their own judgment.

Description: In order for actuaries to play a valuable role in the realm of enterprise risk management ERM, they must provide value-added advice and quantitative analyses. In this paper, the authors use stochastic simulation technology to present a risk metric for defined benefit pension plans that provides improved measures of the plan’s solvency and provides a tool for pension plan managers to determine the value of risk mitigation activities.

Description: The author notes “a telescope and a kaleidoscope both provide a view but that is where the similarities end. A telescope shows us an actual view whereas a kaleidoscope creates a view from broken pieces of glass. This article will analyze which analogy is closer to the stochastic modeling of interest rate or stock market projections.”

Description: Summary of NAIC's Winter National Meeting

Description: We consider a class of compound renewal risk process with claim waiting times have a discrete Km distribution. The classical compound binomial risk model is a special case when m = 1. Both recursive and explicit formulas are derived for the expected discounted penalty function due at ruin, for the surplus before ruin and the deficit at ruin. Many ruin related quantities can be analyzed through the penalty function, e.g., ruin probability, the p.g.f. of the time of ruin, joint and marginal distributions of the surplus before ruin and the deficit at ruin, claim causing ruin, as well as their moments. Detailed discussions are given in two special cases: claim sizes are rationally distributed, or the claim sizes distribution have a finite support.

Description: This is the abstract of the paper 'A Stochastic Definition of Future Shares'. The traditional definition of actuarial future values and stochastic definition of Ramsay are discussed. A modification of Ramsay's definition is proposed and an application to life insurance reserves is presented.

Description: Quantitative operational risk assessment is essentially based on stochastic scenario modeling of operational loss sequences. Given the lack of reliable historical data in most cases, mathematical methods should meet even stronger requirements in terms of results received and include specific features, namely: rare event analysis, uncertainty analysis and human factor analysis, etc. In this paper, the analytical-statistical simulation approach ASSA is considered as the most flexible approach to stochastic scenario loss sequence modeling and compared with Markov chain, fault/event tree and Monte Carlo, in terms of scenario loss sequence model adequacy and calculation cost. Probabilistic risk analysis software PRAISE and some applications are given. Presented at 2010 Enterprise Risk Management Symposium, Society of Actuaries, April 12-15, 2010.