Description: A summary of Modeling Section-sponsored sessions at the 2016 Life/Annuity Symposium, covering model risk management, model governance, and model efficiency.

Description: In this paper, we investigate the dynamics of the Lee-Carter mortality index parameter kt. Specifically, we perform statistical hypothesis tests to examine whether the mortality indexes for Canada, England and Wales and the United States are best described by stochastic trends difference stationary models or deterministic trends trend stationary models. The empirical results favor broken-trend stationary models over difference stationary models, which are used in most previous applications of the Lee-Carter method. The results also give strong statistical evidence that the rates of mortality decline for the three populations have significantly accelerated in mid-1970s.

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: In it’s insurance capital model, Standard & Poor’s Ratings Services has established criteria to adopt the NAIC’s stochastic approach to variable annuity risk. This approach, which replaces existing static charges, better reflects the products’ risk.

Description: Two breakout sessions were held. Their goal was to explore ways in which researchers and practitioners could be brought closer together. The following summaries were edited by Stuart Klugman from notes taken by the indicated participants: Session #1 - Bridging the gap with regard to modality and morbidity and Session #2 - Bridging the gap with regard to financial modeling.

Description: This paper presents a model is which can be used for certain annuities when interest rates and future lifetimes are random. These can be used in determining contingency reserves for possible adverse interest and mortality experience for collections of life annuity contracts. Certain boundary crossing probabilities for the stochastic process component of the model are obtained. From Actuarial Research Clearing House 1991, VOL. 1.

Description: This report describes a stochastic simulation approach used to estimate the amount of a level-payment annuity payable as long as the person is alive and living in his/her house. A discussion of the paper follows. From Transactions of Society of Actuaries 1991, Vol. 43.

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 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.

Description: This paper introduces a rich stochastic modeling framework for understanding risks in multiple-decrement contracts. The example in the paper is a 20-year Term insurance contract. Not only are mortality and lapsation considered stochastic, but the parameters governing them are. For example, mortality risk is composed of four risk elements, including error generated in the underwriting process, volatility around the best estimate, catastrophic events that impact mortality, and the trend in mortality improvement or deterioration. When stochastically modeled, the relative contribution and risk profile of each risk element can be evaluated. Generating stochastic mortality results provides a distribution of results that an organization faces and the severity and incidence of the tail events.