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: In this Chapter we present a novel way for estimating aggregated EC figures based on Bayesian copula estimation. Contrary to the classic approach of using a single inter-risk- correlation matrix we derive a probability distribution of possible correlation matrices that enables us to tackle the important issue of parameter uncertainty. Presented at 2010 Enterprise Risk Management Symposium, Society of Actuaries, April 12-15, 2010.

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: In this paper, a general multivariate duration analysis is introduced that does not depend on a mathematical formulation of the way in which a yield curve moves. To motivate the multivariate approach, simple examples are presented that demonstrate the limitations of the traditional model when yield curve shifts are not parallel.

Description: In this paper, we illustrate how to value American-style options using the Least-Squares Monte Carlo LSM approach proposed by Longstaff and Schwartz 2001 and investigate whether there exists an optimal regression complexity in the LSM framework for options pricing. In particular, we use the smoothing spline in the regression step, which allows us to control the regression complexity on a continuous scale with just one tuning parameter. Numerical results on American put options indicate that we need to use more than a linear regression, but as the regression becomes more complex, the accuracy of the LSM method quickly deteriorates. From 39th Actuarial Research Conference.

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.

Description: 2011 SOA Enterprise Risk Management Symposium, Chicago. This is the abstract of the referenced paper.

Description: Presented at Living to 100 Symposium, January 2011. This research studies coherent mortality modeling by combining a group of populations with similar period effects - e.g., mortality behaviors - in an effort to improve the stability of mortality modeling for older ages.

Description: This paper employs a static-component projection methodology as a first step in a more complex research agenda focusing on developing detailed population projections in which mortality, disability, and disease are represented as linked phenomena with changes in any one impacting the other two. From Retirement Needs Framework, M-RS00-1.

Description: In this paper we shall present our results in terms of the estimation of human mortality rates, but the results carry over to other applications. We shall discuss a Bayesian model that encompasses both graduation [smoothing] and prediction.