This paper surveys the main concepts and techniques of recent developments in the modeling of the term structure of interest rates that are used in the risk management and valuation of interest-rate-dependent cash flows. These developments extend the concepts of immunization and matching to a stochastic interest rate environment. Such cash flows include the cash flows on assets such as bonds and mortgage-backed securities as well as those for annuity products, life insurance products with interest-rate-sensitive withdrawals, accrued liabilities for defined-benefit pension funds, and property and casualty liability cash flows.

Interest Rate Risk Management

• How to choose between competing models for a stochastic phenomenon under investigation. • How to use a standard distribution (mortality, loss, duration, and so on) and client data to obtain an appropriate distribution that is tailored to characteristics of the client. • How to adjust mortality tables in a statistically valid manner to obtain exactly certain known or assumed individual characteristics, while simultaneously developing a table that is as close as possible to a given standard mortality table. • How to graduate or smooth observed insurance data to obtain smoothed estimates that are as close as possible to the observed data, subject to convexity and smoothness constraints. • How to incorporate monotonicity constraints into a life table graduation. This graduation technique can encompass either univariate or multivariate mortality tables with equal facility.

Information theoretic approach to actuarial science: a unification and extension of relevant theory and applications

Operations research methods have been applied to the modeling and the solution of numerous problems in insurance and actuarial science. This paper reviews the applications of these operations research methods in the insurance industry. The paper is organized according to the categorization of operations research methods. Specifically, various mathematical programming models and their applications are first introduced. Game theory and some new operations research approaches are discussed, along with their applications in insurance and actuarial science. The paper concludes with a general discussion of developments and trends in operations research and insurance. For the student who has studied specific operations research techniques mandated by the SOA examination system, this paper provides a set of examples of techniques pertinent to actuaries and shows how the expanding field of general quantitative reasoning in risk management can have a positive impact on the insurance industry. For research actuaries, we finally present an updated bibliography of operations research applications in insurance cross-classified by authors, operations research methodologies, and insurance areas of application.

Operations research in insurance: a review

It is well known that a sufficient condition for the immunization of multiple liabilities is the separate immunization of each liability outflow. This paper proves that this is also a necessary condition. It also discusses how one constructs immunized portfolios by means of linear programming.

Immunization of multiple liabilities

Cash-flow matching, or dedication, is an important and practical tool for managing interest rate risk. This paper applies the duality theory of linear programming to provide insights for generalizing and solving the cash-flow matching problem.

Cash-flow matching and linear programming duality

Shifts in the term structure of interest rates are the major sources of risk to fixed-income portfolios. Two important portfolio investment strategies in asset/liability management are cash-flow matching and immunization. The cash-flow matching strategy can be enhanced by allowing cash carry-forward and borrowing from future surpluses. Although the mathematical program thus formulated is nonlinear, we show that it can be linearized and solved by standard techniques. The algorithms can easily be implemented on a computer.

Rama Kocherlakota

Papers

Algorithms for cash-flow matching