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

Description: Read the April 2020 issue of The Modeling Platform, published by the Modeling Section. Newsletters provide practical information for the working actuary, articles on trends that impact sections and news about section activities.

Description: Read the November 2019 issue of The Modeling Platform, published by the Modeling Section. Newsletters provide practical information for the working actuary, articles on trends that impact sections and news about section activities.

Description: This article is the first installment of a three-part series that aims to provide an overview of ESGs and will focus on the general motivation for stochastic modeling, its advantages and its limitations. Future articles will further break down the key factors of ESGs and the application of these factors to better understand the Academy Interest Rate Generator (AIRG).

Description: Describes using the new multi-risk scenario generator to create sensitivity tests at moderately adverse probability levels, resulting in margins to use for PBR.

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

Description: The April 2016 Issue of The Modeling Platform

Description: The article explores impact of resetting cap vs static cap choice for the GLWB rider for a Fixed Index Annuity for a Point to Point. Moreover, analysis of a Monthly Sum Cap is provided showing impacts of particular choices of market models (e.g. Black, Heston, Bates) used to price this deal.

Description: The next evolution of actuarial systems in the U.S. will likely be a move toward a single system solution. This article defines a single system solution and illustrates how models can be shared across actuarial functions, the potential benefits of a single system solution, and describes potential mitigation strategies to address typical actuarial concerns.

Description: In physics and engineering education, Fermi problems require solutions based on good approximate calculations with little or no actual data, involving making justified guesses and deducing bounds without using sophisticated tools. The idea of Fermi problems are of particular relevance to today's actuaries, as pricing, reserving, and financial reporting involve more and more complex stochastic components. The paper discusses some approximate solutions developed in academia in the spirit of Fermi problems.

Description: Using the recent West Africa Ebola outbreak as an example, the authors discuss several modeling approaches that can be useful for estimating pandemic risk.

Description: This is the User's Guide that accompanies the Inflation Generator Excel spreadsheet which is associated with the research report entitled 'The Effect of Deflation or High Inflation on the Insurance Industry.'

Description: This research report on the effect of deflation or high inflation has six sections: 1. The first section provides background on inflation, describes some problems in measuring inflation, and explains some of its effects on an economy. 2. The second section reviews historical inflation rates. 3. The third section examines the effect of inflation or deflation on the property-liability and life insurance industries. 4. The fourth section proposes risk mitigation strategies for insurers to cope with either deflation or high inflation rates. 5. The fifth section describes a publicly available model that can be used to develop inflation/deflation projections under a regime switching format that can readily be adjusted to reflect current financial uncertainty. 6. The sixth section provides conclusions.

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: Feature article discussing how insurers have reflected volatility in asset return assumptions when determining capital requirements, but have largely disregarded the impact of mortality volatility on their liability assumptions when performing stochastic analysis.

Description: Discusses methods to efficiently run stochastic models in light of AG 43.

Description: Discusses the interactions between dynamic lapses and interest rates in stochastic modeling for variable annuities.

Description: In the copula literature there are many bivariate distribution families but very few higher dimensional ones. Moreover, most of these are difficult to work with. Some of the bivariate families can be extended to more dimensions but in general the construction of distribution functions with more than two variables is a difficult problem. This paper introduces a construction method that is straightforward to implement and can produce multivariate distribution functions of any dimension.

Description: This paper discusses some of the models used to quantify risk, note some areas where improvements in standard methods are needed, and in some cases suggest alternative approaches for risks in Property and Casualty Insurance and Life Insurance.

Description: The research investigates the challenges associated with determining a “fair value” assessment for embedded options in two product types and incorporates the process into product pricing and liability valuation

Description: This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross-section of risk classes towns with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution like univariate t-distributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

Description: This paper discusses the theoretic framework of modeling captial markets: index-based composition methodology and statisical procedure of model construction and extension: wavelets-based financial signal processing technique. It also discusses the implications and applications, measuring the market uncertainty and volatility highlighting the S&P 500 as an example.

Description: This paper develops a new technique, which allows the analyst to maximally use all thte historical interest rate information available in forecasting interest rates. Interest rates' daily change do not follow a stationary random process over long time periods. Instead, the process is comprised of stationary periods, each a few years long, with relatively short transitional periods between different stationary periods.

Description: This paper examines some new Bayesian models for loss reserving inspired by a consideration of some of the methods and techniques appearing in the traditional chain ladder literature. This includes a possibly order restricted hierarchical Bayesian model for the year over year development factors. The issues of reserve variability and ranges of reasonable reserve estimates are considered. A new Bornhuetter-Ferguson styled Bayesian method of estimate revision is also discussed. These Bayesian models can be implemented using Markov chain Monte Carlo MCMC methods in a variety of programming languages, and can serve as starting points for more advanced models. This paper describes their implementation in WinBUGS a specialized software program for MCMC simulations. Illustrative WinBUGS code is included.

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 incorporates a jump-diffusion process into the original Lee-Carter model, and uses it to forecast mortality rates and analyze mortality securitization.

Description: Appendix to the Critical Review of Stochastic Simulation Literature and Applications for Health Actuaries. The Development of a Simulation Model of Primary Prevention Strategies for Coronary Heart Disease

Description: A study on stochastic simulation literature as it applies to a health actuary.

Description: This paper is Part 1 of a two-part submission. Part 2, “An Alternative Approach to Capital Allocation,” discusses using risk-replicating techniques that directly calculate the cost of capital. Such techniques can be used as a substitute for capital allocation. This paper expands upon current capital analysis by introducing a practical approach that considers the objectives of all stakeholders of an insurance company in setting appropriate capital targets.

Description: This paper first derives the fair participation rate based on a fair value of the equity-indexed annuity EIA. Then using risk measures, a new participation rate is obtained, based on the tail loading of the hedging error distribution. Risk management strategies reducing risk related to the hedging error are also presented. A detailed numerical analysis is performed for a point-to-point EIA.

Description: The purpose of this discussion is to introduce a few additional points and discuss how different assumptions will alter the results in some cases.

Description: This paper analyzes the optimal retention level with a portfolio of insurance risks, and premiums invested in risk-free and risky assets. Optimality is defined here as maximizing expected utility of terminal payout.

Description: Presentation at the 41st Actuarial Research Conference held on August 10-12, 2006 in Montreal, QC. This paper considers the problem of extending regime-switching models for asset returns to the situation with multiple asset markets. The conditional tail expectation CTE is highly sensitive to the assumed dependence structure between the regime models for the different markets. A Monte Carlo simulation is used to illustrate the cost of misspecification. The authors find that the model most commonly used by practitioners is worse than all of the alternatives that they investigate.

Description: Are Your Scenarios on Target?From Risks and Rewards Newsletter, August 2005, Issue No. 47. Actuaries are faced with the dilemma of how to incorporate advances in insurance products and modeling technology into their work. Increasingly, this means looking at a large number of potential outcomes using stochastic simulations.

Description: Presented at May 2005 Spring Meeting. Panelists discuss the use of stochastic embedded value 'EV' in financial management and risk measurement, including considerations in reconciling period-to-period results.

Description: Panelists discuss economic capital, capital modeling, and hedge modeling, especially for guaranteed living benefits [GLBs] on variable annuities. Session 34PD of the 2005 Valuation Actuary Symposium.

Description: From a session at the Spring meeting of the Society of Actuaries held in San Antonio, Texas, June 14-15, 2004 The panelists discuss the benefits of hedging variable annuity guarantees, the challenges they face and how they keep score.

Description: From a session at the Spring meeting of the Society of Actuaries held in San Antonio, Texas, June 14-15, 2004 This session discusses emerging capital and reserve requirements on Variable annuities with guaranteed benefits and the effect that hedging/capital management strategies can have.

Description: The panel demonstrates a technique that can help set confidence intervals regarding future rate increases used to satisfy the NAIC rate stabilization model. Specific topics include creating a stochastic model, deciding which variables are deterministic vs. stochastic, developing probability distributions for the stochastic variables, running the model and evaluating the reasonableness of results. From the Record of the Society of Actuaries, Volume 30, No. 1, Session 21

Description: This paper represents a brief progress report on research, being sponsored by the Casualty Actuarial Society and the Society of Actuaries, in the area of modeling of economic series. In particular, research is being undertaken to provide a foundation for the actuarial community’s modeling of a variety of economic variables, including interest rates, equity returns, inflation, unemployment rates, and real estate price levels. The specific objectives of this research are to provide a summary of the literature in the area of economic scenario modeling, identify data sources and methodologies in this area useful to the actuarial profession, and produce working software for economic modeling, including appropriate documentation, to be made available to the general actuarial community in order to allow actuaries to use and build upon this research. From Actuarial Research Clearing House 2004, Vol. 1.

Description: This session from the 2003 SOA Orlando Meeting discusses the new risk-based capital RBC requirements for variable annuities with guranteed benefits such as guaranteed minimum death benefits - GMDBs and guaranteed minimum income benefits - GMIBs. From the Society of Actuaries Record, Volume 29, No. 3.

Description: An Overview of Stochastic Simulation modeling techniques and usages

Description: Discussion of Capital Market Modeling techniques

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: This presentation is a Teaching Session, number 30TS, from the 2002 Valuation Actuary Symposium, held September 19-20 in Lake Buena Vista, FL. The panelists discuss modeling issues for products with embedded options, such as minimum living or death benefit guarantees on variable life and annuities, and annuity death benefit enhancements. They discuss the risks posed by these features and products, selecting realistic dynamic assumptions, techniques used in modeling these features and products, stochastic analysis, and presenting results to best communicate risks clearly. Discussion from participants is included.

Description: This session at the SOA 2001 Toronto Spring Meeting offers an overview of stochastic pricing including stochastic variables, equity market models, interest rate models and policyholder behavior. An example is given using a variable annuity product.

Description: This presentation is a panel discussion, session number 9PD, from the 2000 Valuation Actuary Symposium, held September 14-15 in Washington, DC. A fundamental assumption in stochastic asset/liability modeling is the underlying economic scenario generator. In this session the panelists discuss various scenario generation techniques, assumptions underlying bond and equity scenario generators, and choosing suitable economic scenario generators for different applications. Discussion from participants is included.

Description: From a session at a meeting of the Society of Actuaries held in San Diego, CA, June 22-23, 2000 A discussion of how stochastic modeling techniques can be used to efficiently and effectively consider a wide variety of scenarios and outcomes and how these tools can be used to optimize portfolio performance?

Description: The purpose of this paper is to present to the actuarial profession a stochastic investment model which can be used for simulations extending for many years ahead. Discussed in the paper are the general reasons for choosing the style of model, the general model and how to use it, the assumptions and the sensitivity of model to the assumptions made and the possible applications in the investment and actuarial fields.

Description: From a session at the Spring regional meeting of the Society of Actuaries held in Atlanta, Georgia, May 24-25, 1999 Equity-indexed products require an asset strategy that matches the equity options embedded in the liability. The panel discusses the following: A. Two asset strategies 1. Purchasing equity options that match the liability options: Is this a perfect match or are there still unhedged risks? 2. Dynamic hedging using the mathematics of “the Greeks”: Is it self-insuring? B. Accounting issues with these strategies

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: Panelists at this session of the SOA 1998 Maui II Spring Meeting present methods for scenario generation and establishing stochasitc models for pension plans.

Description: 1998 Valuation Actuary Symposium. The panelists discussed how asset liability management is synonymous with a dynamic financial analysis and quantitative risk management. Topics covered were systems implementations including asset risk exposure optimization given a company-specific set of liabilities and total risk exposure optimization, which includes stochastic analysis of alternative asset and liability strategies.

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: This paper addresses the evaluation of long-term returns when the short interest rate is modeled by a general diffusion process. By deriving the long-term return dynamics and invoking the Feyman-Kac formula, the long-term return is represented as the solution of a partial differential equation. A finite difference method is derived for the valuation of the long-term return. The method could be used for hedging interest rate risk, pricing and managing interest rate derivatives and interest rate sensitive insurance products. Numerical examples are included.

Description: This paper presents a new methodology for obtaining fast algorithms and closed form solutions for pricing callable bonds in continuous time models. Results are directly applicable to regulatory scenario testing, immunization and market value accounting.

Description: This session from the 1995 SOA Boston Meeting discusses constructing and using a comprehensive, credible risk management system with a concentration on C-3 risk. It also covers an example of option adjusted spread analysis for a single premium deferred annuity SPDA. From the Record of the Society of Actuaries, Vol. 21, No. 4b.

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: 1994 SOA Spring Meeting, Orlando. In this session the panel consider the question of uncertainty in loss reserves including discussion of sources and measurement. The panelists analyzed the same data set from different perspectives and discussed the strengths and weaknesses of the approaches.

Description: Provides a how-to session on modeling assets and liabilities in the Valuation Actuary's work to comply with the Standard Valuation Law. Comparisons of the methods discussed are occasionally made with the requirements of New York Regulation 126. Session 12 of the 1991 Valuation Actuary Symposium.

Description: This section contains multiple book reviews and notices concerning the actuarial profession. Reviews: 'Medical Risks: Patterns of Mortality and Survival' by Singer and Levinson, 'The Theory and Practice of Pension Funding' by Trowbridge and Farr, 'Two Stochastic Processes' by Beekman, 'Disability Income Insurance - Cost Differentials between Men and Women' by New York Insurance Department, 'Social Security and Private Pension Plans: Competitive or Complementary' by McGill, 'A New Look at Accounting for Pension Costs' by Hall and Landsittel, '1977 Annual Reports of the Board of Trustees of the Federal OASDI Trust Funds...,' 'Investigation of Sickness Statistics - Individual Policies, 1971 and 1973' by the Institute of Actuaries and the Faculty of Actuaries, 'The Graduation of Pensioners and of Annuitants Mortality Experience 1967-70' by the Institute of Actuaries and the Faculty of Actuaries, 'Pensions and Survival - the Coming Crisis of Money and Retirement' by Calvert, 'Group Benefits in a Changing Society' by Spencer, 'Experience of Disabled Work Benefits under OASDI 1965-74' by Bayo and Wilkin. Digests also included.

Description: In this paper, a mathematical model is constructed to study the deviations of claims, investment performance, operating expenses, and lapse expenses as random stochastic processes. Discussions of the paper submitted by 2 readers follows