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: Summary of NAIC's Winter National Meeting

Description: Discussion of how to obtain tight upper and lower bounds on E[hX] for a given function h, and a random variable X with three known moments.

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: 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: This article looks at stochastic techniques actuaries can use to quantify the non-market risks in insurance products and how stochastic techniques can be used in the evaluation of reinsurance arrangements.

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

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.