using utility theory for describing best estimate reserves mark w. littmann 1998 casualty loss...
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Using Utility Theory for Describing Best Estimate
Reserves
Mark W. Littmann
1998 Casualty Loss Reserve SeminarPhiladelphia, Pennsylvania
“Best” - as an adjective
Superlative form of “good” Surpassing all others in excellence,
achievement, or quality Most satisfactory, suitable, or useful;
most desirable
Utility Theory Framework
Under certainty Under uncertainty
Relevance for Reserving
Utility is about preferences Decision making is about maximizing
utility Different parties will have different
preferences for different reserve estimates
Relevance for Reserving
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 Reserving actuary Regulators Auditors Shareholders and investors Wall Street analysts and rating agencies Senior management
View of an Actuary
Seeks the right answer With a degree of conservatism Does not forget prior estimate(s)
Actuary’s Utility Curve
0
20
40
60
80
100
120
Low Mid-point
A High
Actuary’s Utility Curve
0
20
40
60
80
100
120
Low Mid-point
A High
Actuary’s Utility Curve
0
20
40
60
80
100
120
Low Mid-point
A High
Actuary’s Utility Curve
0
20
40
60
80
100
120
Low Mid-point
A High
View of a Regulator
Ensure that policyholders’ and claimants’ demands are satisfied; that is, maintain solvency
Prudence and conservatism Greater reserves are preferable,
because bad outcomes need to be protected against
Regulator’s Utility Curve
0
20
40
60
80
100
120
140
Low Mid-point
High
View of an Auditor
Overall financial statements Interaction between balance sheet and
income statement Materiality considerations Movements within a range of
reasonable estimates
Auditor’s Utility Curve
0
20
40
60
80
100
120
140
Low Mid-point
High
View of Shareholders and Investors Do not like surprises Consistency in earnings growth is
rewarded Sometimes a 1-time large hit is rewarded Maximum utility is assigned to the
reserve that maximizes the valuation of the enterprise
View of Wall Street Analysts and Rating Agencies Objective is to assess financial strength
and ability to generate future earnings Maximum utility is associated with the
“right answer,” perhaps anticipating an action before it happens
View of Management -Public Company Must balance myriad of interests Different members of management may
have different views– claims, underwriting, finance, executive
To set a formal policy or not?
Public Company Management’s Utility Curve
0
20
40
60
80
100
120
Low Mid-point
High
View of Management -Private Company Reduced pressures from outside parties May focus on strength of balance sheet May focus on maximizing dividend
potential May consider earnings stream in
anticipation of a public offering
Private Company Management’s Utility Curve
0
20
40
60
80
100
120
Low Mid-point
High
Company Management - New Faces Utility of reserve estimates in year-1
may be influenced by circumstances surrounding the change
Decision Process
Can only record one amount Must integrate the relative preferences Relative power of the parties Relative shapes of utility curves Influence of absolute constraints
Example
1996 basically an average year Pressure to show better results in 1997 Slight deterioration in actuarial reserve
estimates
Detailed background contained in the paper
Actuary’s Utility Curve
0
50
100
150
200
250
82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
Actuary
Actuary's Max Utility
Management Utility Curve
0
50
100
150
200
250
82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
Management
Management's Max Utility
Aggregate Utility Curve
0
50
100
150
200
250
82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
Aggregate Management Actuary
Actuary's Max Utility
Management's Max Utility
AggregateMax Utility
Summary
A best-estimate reserve is the value for which the aggregate utility of the interested parties is maximized.
Closing Remarks
What is “Best?” What is “Fair?” Utility theory framework is useful Utility curves vary by party and may
vary over time Aggregation function of utility curves
Closing Remarks
What is “Best?” What is “Fair?” Utility theory framework is useful Utility curves vary by party and may
vary over time Aggregation function of utility curves
The Negotiation Process
Discussion