CAS Ratemaking Seminar Rick Anderson Pricing Catastrophe Reinsurance With Reinstatement Provisions Using a Catastrophe Model CAS Ratemaking Seminar Rick Anderson Chief Actuary March 11, 1999

Introduction Reinstatement provisions Event Loss Table (ELT) Reinstatements limited by aggregate losses Summary © 1999 Risk Management Solutions, Inc.

Reinstatement Provisions Based on number of occurrences or aggregate losses Free or paid Pro rata to full limit Pro rata to full time © 1999 Risk Management Solutions, Inc.

Event Loss Table Basic output of catastrophe model A table listing the possible events that affect the portfolio, along with the associated frequency and severity information © 1999 Risk Management Solutions, Inc.

Event Loss Table © 1999 Risk Management Solutions, Inc.

Reinstatements Limited by Aggregate Losses Estimating the expected loss requires the aggregate loss distribution Panjer’s recursive approach Fourier transforms Simulation © 1999 Risk Management Solutions, Inc.

Aggregate Loss Distribution © 1999 Risk Management Solutions, Inc.

Limited Expected Value © 1999 Risk Management Solutions, Inc.

Expected Loss for the Treaty © 1999 Risk Management Solutions, Inc.

Expected Premium © 1999 Risk Management Solutions, Inc.

Fair Up-Front Premium Rate Set expected premium equal to expected loss: Solve for R: © 1999 Risk Management Solutions, Inc.

Comparison of Results © 1999 Risk Management Solutions, Inc.

Summary © 1999 Risk Management Solutions, Inc.