Bootstrapping • Identify some of the forces behind the move to quantify reserve variability. • Review current regulatory requirements regarding reserves and how they have been traditionally addressed. • Walk through an example of the traditional chain- ladder reserving approach. • Contrast the differences between the chain-ladder and bootstrap approaches (or deterministic and stochastic models more generally). • Walk through an example of a Bootstrap iteration.
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Bootstrapping Identify some of the forces behind the move to quantify reserve variability. Review current regulatory requirements regarding reserves and.
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Bootstrapping• Identify some of the forces behind the move to quantify
reserve variability.
• Review current regulatory requirements regarding reserves and how they have been traditionally addressed.
• Walk through an example of the traditional chain-ladder reserving approach.
• Contrast the differences between the chain-ladder and bootstrap approaches (or deterministic and stochastic models more generally).
• Walk through an example of a Bootstrap iteration.
All Booked Reserves are “Estimates” of the Ultimate
Liability.
Partial List of Sources• CAS Working Party on Quantifying Variability in Reserve
Estimates. The Analysis and Estimation of Loss & ALAE Variability: A Summary Report. CAS Forum (Fall 2005): 29-146.
• England, P. D. and R. J. Verrall. 2002. Stochastic Claims Reserving in General Insurance. British Actuarial Journal 8:443-544.
• Kirschner, Gerald S., Colin Kerley, and Belinda Isaacs. Two Approaches to Calculating Correlated Reserve Indications Across Multiple Lines of Business. CAS Forum (Fall 2002): 211-46.
Reserve Estimation Variability• Actuaries dissatisfied with “point estimates”.
• Companies Developing ERM Practices.
• Technology Allows for Company Simulations.
• Rating Bureaus (like AM Best) and Regulators have an interest in Reserve Variability.
RED ALERT!!
Australia’s Prudential Regulatory Authority:
“Technical Reserves To Be Determined as the Present value of a Central Estimate, with a Risk Margin to approximate the 75% Confidence Level.”
Statements of Statutory Accounting Principles
• “Management’s best estimate” of its liabilities is to be recorded.
• Accrue the midpoint of range when no single estimate is better than any other.
• Accrue best estimate by line of business. Redundancies in one line cannot offset inadequacies in another.
Statement of Actuarial Opinion • Governed by Actuarial Standard of Practice
(that is ASOP) 36.
• When reserve is within “range of reasonable estimates”, it is assumed the reserve is reasonable.
• Range of Reasonable Estimates determined by appropriate methods or sets of assumptions judged to be reasonable.
Historically, the Range of Reasonable Estimates have been developed by varying methods and/or assumptions,
NOT by using statistics to evaluate the loss distribution.
• Allows for the estimation of the Probability Distribution.
Stochastic models complement
Deterministic methods by providing more
information on the possible outcomes.
Bootstrapping
• Resampling with Replacement Method• Incorporates Parameter Variance• Incorporates Process Variance• Cannot Incorporate Model Uncertainty (but
no model can)
Bootstrapping
• Resamples Pearson Residuals
• Relies on the “Over-Dispersed Poisson Distribution” Which Can Model the Traditional Link Ratio Method
• Thus, a Generalized Liner Model Underlies the Traditional Link Ratio Method
The Gamma Distribution• Used in place of Over-Dispersed Poisson Distribution in Bootstrapping• Models Process Variance in Bootstrapping• Sum of n exponentially distributed random variables• Described by a shape parameter and a scale parameter • Mean = , Variance = 2