Using Utility Theory for Describing Best Estimate Reserves Mark W. Littmann 1998 Casualty Loss Reserve Seminar Philadelphia, Pennsylvania

“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

Utility Theory Framework n Under certainty n Under uncertainty

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

Relevance for Reserving n Utility of a reserve amount is a function of the party’s: –relationship to the reserves –motivations and self-interests

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

View of an Actuary n Seeks the right answer n With a degree of conservatism n Does not forget prior estimate(s)

Actuary’s Utility Curve

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

Regulator’s Utility Curve

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

Auditor’s Utility Curve

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

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

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?

Public Company Management’s Utility Curve

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

Private Company Management’s Utility Curve

Company Management - New Faces n Utility of reserve estimates in year-1 may be influenced by circumstances surrounding the change

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

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

Actuary’s Utility Curve

Management Utility Curve

Aggregate Utility Curve

Summary n A best-estimate reserve is the value for which the aggregate utility of the interested parties is maximized.

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

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

Discussion