Casualty Actuarial Society

Meeting and Seminar Handouts

2003 Thomas P. Bowles Jr. Symposium

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Keynote Presentation by the Bowles Chair --- Key Issues and Mission

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Wang will discuss current major research issues in risk measurement, capital cost allocation, and fair valuation of liabilities, as introduced in the 2003 Bowles Symposium Call for Papers Program. Wang will offer his perspectives and research findings on how to address these issues. He will also introduce the assembled scientific program of the Symposium and layout ground rules for interactive discussions.

Risk Measures and Capital Allocation Methods—An Overview
Speaker: Gary G.Venter

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In this presentation Venter will summarize various risk measures, including Rodney Kreps's co-measures. He will also present a categorization of four methods of capital allocation.

A Risk Charge Calculation Based on Conditional Probability
Speakers: David L. Ruhm and Donald F. Mango

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Insurers experience the realization of risk in the form of aggregate portfolio results. Yet, it is often necessary to assess the risk contributed by individual components, such as lines of business, and to directly (or effectively) allocate the total portfolio risk to the components. A method will be presented that measures a component's risk in terms of that component's contributions to potential aggregate outcomes. Risk charges calculated in this way are additive, and the resulting prices are consistent in the arbitrage-free sense. The theory underlying this method produces a mathematical relationship between market pricing of risk and the cost of risk to an individual agent.

The Economics of Capital Allocation
Speaker: Glenn G. Meyers

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On the surface, capital allocation seems contradictory to the stated purpose of insurance, i.e. diversifying risk, but it is commonly used as a tool by insurers to manage their underwriting risk. This paper examines the economics underlying how insurers might use capital allocation. Starting with a coherent measure of risk, the paper will establish that the marginal capital serves as a lower bound for allocated capital. Then through a series of propositions and examples, the paper shows when it is appropriate to deviate from this lower bound.

Why Can Financial Firms Charge for Diversifiable Risk?
Speakers: Andrew Smith, Ian Moran, and David Walczak

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It is widely accepted that capital markets do not demand a premium for risk that investors can diversify. On the other hand, insurers' and banks' pricing models frequently include an allowance for total risk, diversifiable or not. This raises the puzzle of why competitive product markets do not eliminate these pricing margins. This paper proposes an answer to the puzzle, involving the frictional costs that financial institutions incur in the course of their risk-bearing function. A series of worked examples demonstrate the implications for pricing, risk management, and financial reporting.

The Winner's Curse: A Basic Truth in the Insurance Market
Speakers: Christian Svendsgaard, Robert Downs and Shaun Wang

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In the (re)insurance market, the same risk can receive price quotes from multiple insurers. Some insurers will quote low and others will quote high, due to errors in cost estimation and/or different market strategies. Usually the lowest price bidder will get the business. There is a good chance that the winner will underestimate the true cost, and thus be cursed by financial losses. We will discuss how the Winner’s curse should change the way that actuaries model risks, and how companies can break the spell of the Winner’s Curse. Further, we will discuss how it would change our view on diversification benefits between lines of business and the cost of capital.

Pricing and Capital Allocation for Unit-Linked Life Insurance Contracts with Minimum Death Guarantee
Speakers: Christophe Frantz, Xavier Chenut, and Jean-François Walhin

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Concentrating on the minimum death benefit guarantee associated with unit-linked life insurance contracts, the authors aim to price that cover. In their paper they build a cash-flow model similar to what is used in evaluating any investment decision. The premium is then determined in such a way that the discounted value of all the cash flows is equal to zero. The distribution of the future losses at any future time.

allows one to obtain the provisions and the capital required to back this business. This finally raises the question of the amount of capital needed. This question, particularly for the present multi-period case, does not yet have a definitive answer in the literature.

Marginalizing the Cost of Capital
Speakers: Daniel B. Isaac, Nathan J. Babcock

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Typical actuarial discussions about cost of capital focus on the best method for allocating these costs. Unfortunately, the need for this allocation is in direct contrast with modern finance theory: only monopolies price products based on their average costs, the rest use marginal. The authors of this paper will investigate whether a new approach to determining the cost of capital, as well as other related items, can eliminate this apparent discrepancy.

Pricing Issues in Aviation Insurance and Reinsurance
Speaker: Morton N. Lane

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Aviation insurance covers events that are catastrophic in nature—the loss of aircraft and passengers can be extraordinarily costly—and yet it is conducted in a manner different from traditional property/casualty catastrophe insurance. Ground-up insurance cover is provided on an unlimited sideways basis for "each and every loss." For example, it is provided on an unlimited aggregate basis. Reinsurance, however, is not provided on a ground-up basis and it is only provided with strict limits of liability. How should such exposures be priced? What returns can be expected? How should insurance rates relate to reinsurance prices? Also, capital providers always have the alternative of deploying their capital to other forms of risky endeavors, whether in insurance or other markets. How, then, should aviation insurance prices relate to other risk-prices? The paper reviews the pricing issues particular to aviation and relates them to prices and returns in other markets.

The Effect of a Company's Credit Standing on the Measurement of Fair Value
Speakers: Sam Gutterman and Mo Chambers

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For those financial institutions who will prepare their financial statements according to International Accounting Standards (IASB) or U.S. GAAP in the next couple of years, it is possible that a considerable amount of their liabilities may have to be measured on a fair value basis. According to U.S. GAAP Concept Statement No. 7 and tentative conclusions reached by the IASB in January, the reported value of financial liabilities will be reduced by a factor that corresponds to the company's credit standing, similar to what is done with certain assets. This paper explores the practical issues associated with this factor that has proven quite controversial. It includes a discussion of the interests of the various users of financial statements, the advantages and disadvantages of applying such a factor, and some of the practical difficulties associated with this factor.

Credit Standing and Fair Value of Liabilities: A Critique
Speaker: Philip E. Heckman

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Heckman will review the positions of major accounting and actuarial bodies on the issue of whether the holder's own credit standing should be reflected in the fair value of its liabilities, identifying certain anomalies, both in the current GAAP treatment of debt and in the FASB proposal for fair valuation of liabilities. The paper proposes an alternative approach that stresses the need for an objective valuation standard, based solely on contractual terms and ambient economic conditions. This approach yields readily interpretable public information. Finally the paper will review the probable consequences if, as seems likely, the FASB proposal prevails.

The Impact of Credit Risk on Fair Valuation of a Liability
Speaker: Trent R. Vaughn

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Vaughn's paper will describe the impact of credit risk on determining the fair value of a liability. The paper will explore the problem of determining the fair value of a (generic) liability from first principles, using standard financial valuation theory. Vaughn will discuss the approach to fair value described in the recent American Academy of Actuaries (AAA) monograph, including a critique of the credit risk comments in that monograph. The author will also provide a link between the "cost of capital method" for fair valuation (as described in the AAA monograph) and the more common property/casualty actuarial approach of "risk loads." Vaughn will conclude by emphasizing the need for sound actuarial judgment in determining the fair value of an insurance liability.

Unsolved Problems in Financial Science
Speaker: Donald F. Mango

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Financial science is a converging field with roots in finance, financial economics, economics, financial engineering, insurance, and actuarial science. It is the study of contingent financial activities (loans, insurance policies, bonds, derivatives, stocks), and their structure, valuation, sale, exchange, accumulation, and interaction. As this science inches toward existence, it faces fundamental problems that must be addressed, similar to other sciences at their origins. Mango will highlight his own opinion of the critical problems to be addressed, and suggest priorities and tactics for research.

 Application of Advanced Science in the New Era of Risk Modeling
Speakers: Lee Smith and Lilli Segre Tossani

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This paper describes the workings of the new sciences of complexity and chaos theory as applied to practical problems in the insurance industry. In particular, the fair valuation of insurance liabilities will be addressed in the context of these new areas of thought. Scientists in the Santa Fe and Los Alamos, New Mexico communities have developed data mining, analytical, and visualization tools that supersede traditional methods in various areas, including the quantification of risk and uncertainty. The paper will survey the global risk landscape and show how these new tools create a paradigm shift in areas like the valuation of insurance contingencies.

Combined Functionals as Risk Measures
Speaker: Dr. Arcady Novosyolov

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Risk measures are widely used in insurance pricing, portfolio selection, and in decision-making in general. Two prevalent classes of risk measures are expected utility (a dollar transform), and distorted probability (a probability transform). Both approaches exhibit properties that are not supported by empirical evidence on decision-making under risk. The author proposes a combined functional (dollar and probability transform) that may combine the best properties of both approaches. The paper will develop representation theorems and axiomatic descriptions; present applications to decision-making under risk, premium calculation, and portfolio selection; and include numeric and graphical illustrations.

Equity Risk Premium: Expectations Great and Small
Speakers: Richard Derrig and Elisha Orr

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The Equity Risk Premium (ERP) is an essential building block of the market value of risk. Since Mehra and Prescott's 1985 article, "The Equity Premium: A Puzzle," there has been a constant stream of research, all of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about minus one percent to about nine percent, according to the horizon, short- or long-term, the short- or long-run expectation, and the geometric or arithmetic estimate. This paper will examine the principal strains of the recent research on the ERP and catalogue the empirical values of the ERP implied by that research. In addition, the paper will supply several time series analyses of the standard Ibbotson Associates 1926-2001 ERP data using short treasuries for the risk-free rate.

Basel-Type Capital Requirements for Insurers: Report by IAA Insurer Solvency Assessment Working Party
Speakers: Harry Panjer


Distortion Measures and Economic Capital
Speaker: Werner Hürlimann

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To provide incentive for active risk management, it is argued that a sound coherent distortion measure should preserve some higher degree stop-loss orders, at least the degree three convex order. Such risk measures are called free of tail risk or simply tail-free risk measures. It is shown that under some common axioms and other plausible conditions, a tail-free coherent distortion measure identifies necessarily with the Wang right-tail measure or the expected value measure. This main result is applied to derive an optimal economic capital formula.

Guaranteed Annuity Conversion Options and Their Valuation
Speakers: Laura Ballotta and Stephen Haberman

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We consider a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain unit-linked pension contracts in the UK. The valuation approach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of one-factor Heath-Jarrow-Morton framework for the term structure of interest rates, in order to obtain a closed-form analytical solution to the fair valuation of the liabilities implied by these contracts. Mortality risk is incorporated via a stochastic model for the evolution over time of the underlying hazard rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the key financial and mortality parameters is also analyzed.

Perspectives on Future Directions
Moderator: Shaun S. Wang

Invited Discussion by William H. Panning
Invited Discussion by Stephen W. Philbrick - Download Paper
Other Invited and Open Discussions
Wrap Up— What Have We Accomplished & Where Do We Go From Here?

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