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 paper focuses on the fact that life and annuity reserves that are determined from discounted case flows mask the dynamic nature of interest rates. To study this effect in a stochastic interest environment, the authors look at a change in discounted reserves. By looking at the appropriate measure of change, the paper explores potential short-term consequences of changes in the interest environment.

Description: The main aim of this paper is to apply some of the techniques of modern time series and econometric analysis to analyse investment data in order to better understand the nature of long run relationships in investment series typically used in stochastic investment models. The paper attempts to identify and address fundamental issues that need to be considered before developing a particular stochastic investment model.

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: 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.

Description: Stochastic approximation is a powerful tool for sequential estimation of zero points of a function. In this paper, this methodology is defined and is shown to be related to a broad class of credibility formulae derived for the Exponential Dispersion Family. The authors further consider a Location Dispersion Family which is rich enough and for which no simple credibility formula exists. For this case, a Generalized Sequential Credibility Formula is suggested and an optimal stepwise gain sequence is derived.

Description: Design and future maintenance of an asset portfolio backing a new line of business is critical for proper asset and liability management for that business. Most portfolio optimization methods utilize linear or quadratic programming and require the user to specify the asset and liability attributes and cash flows into the program. The programmer must also supply an objective function to allow the program to find the optimal asset mix for the associated liabilities. Two problems with this approach are that the liability cash flows are fairly static and that one must frequently rebalance the portfolio. An alternative approach would be to develop a corporate model of both the assets and liabilities and incorporate various economic scenarios as input into the model. Asset strategies would be measured against a specific objective function that is calculated by the corporate model. Unfortunately, the majority of maximization algorithms available are very time consuming, and obtaining a reasonable portfolio mix becomes impractical. This paper overcomes this difficulty by using a very rapid optimization method from the chemical engineering profession called the Floppy Triangle. The paper includes an example of the use of this process to determine an optimal portfolio. It also discusses modifications of the algorithm that is required when the shorting of assets is not permitted.

Description: Feature article discussing numerical short cuts, rules of thumb, estimators, modeling tips, etc. The featured problem is fitting the intermediate points for a real-world stochastic model of interest rates.

Description: 2011 Enterprise Risk Management Symposium, Chicago. This study investigates whether simulation-based models can be used to predict liquidity risk for banks, which must comply with Basel III by January 2015. The paper looks at the process of developing a measurement framework using Black-Scholes and Merton’s asset-based models to measure liquidity risk.

Description: An overview of guaranteed lifetime withdrawal benefits (GLWB) on registered index-linkedannuity (RILA) products and a stochastic analysis of market risks.