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Using Utility Theory for Describing Best Estimate Reserves Mark W. Littmann 1998 Casualty Loss Reserve Seminar Philadelphia, Pennsylvania
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“Best” - as an adjective n Superlative form of “good” n Surpassing all others in excellence, achievement, or quality n Most satisfactory, suitable, or useful; most desirable
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Utility Theory Framework n Under certainty n Under uncertainty
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Relevance for Reserving n Utility is about preferences n Decision making is about maximizing utility n Different parties will have different preferences for different reserve estimates
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Relevance for Reserving n Utility of a reserve amount is a function of the party’s: –relationship to the reserves –motivations and self-interests
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Parties with an Interest in Reserves n Reserving actuary n Regulators n Auditors n Shareholders and investors n Wall Street analysts and rating agencies n Senior management
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View of an Actuary n Seeks the right answer n With a degree of conservatism n Does not forget prior estimate(s)
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Actuary’s Utility Curve
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View of a Regulator n Ensure that policyholders’ and claimants’ demands are satisfied; that is, maintain solvency n Prudence and conservatism n Greater reserves are preferable, because bad outcomes need to be protected against
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Regulator’s Utility Curve
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View of an Auditor n Overall financial statements n Interaction between balance sheet and income statement n Materiality considerations n Movements within a range of reasonable estimates
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Auditor’s Utility Curve
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View of Shareholders and Investors n Do not like surprises n Consistency in earnings growth is rewarded n Sometimes a 1-time large hit is rewarded n Maximum utility is assigned to the reserve that maximizes the valuation of the enterprise
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View of Wall Street Analysts and Rating Agencies n Objective is to assess financial strength and ability to generate future earnings n Maximum utility is associated with the “right answer,” perhaps anticipating an action before it happens
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View of Management - Public Company n Must balance myriad of interests n Different members of management may have different views –claims, underwriting, finance, executive n To set a formal policy or not?
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Public Company Management’s Utility Curve
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View of Management - Private Company n Reduced pressures from outside parties n May focus on strength of balance sheet n May focus on maximizing dividend potential n May consider earnings stream in anticipation of a public offering
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Private Company Management’s Utility Curve
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Company Management - New Faces n Utility of reserve estimates in year-1 may be influenced by circumstances surrounding the change
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Decision Process n Can only record one amount n Must integrate the relative preferences n Relative power of the parties n Relative shapes of utility curves n Influence of absolute constraints
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Example n 1996 basically an average year n Pressure to show better results in 1997 n Slight deterioration in actuarial reserve estimates Detailed background contained in the paper
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Actuary’s Utility Curve
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Management Utility Curve
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Aggregate Utility Curve
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Summary n A best-estimate reserve is the value for which the aggregate utility of the interested parties is maximized.
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Closing Remarks n What is “Best?” What is “Fair?” n Utility theory framework is useful n Utility curves vary by party and may vary over time n Aggregation function of utility curves
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Closing Remarks n What is “Best?” What is “Fair?” n Utility theory framework is useful n Utility curves vary by party and may vary over time n Aggregation function of utility curves The Negotiation Process
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Discussion
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