Analysis of IBNR Liabilities with Interevent Times Depending on Claim Counts

Area of Science:

• Actuarial science
• Financial mathematics
• Risk management

Background:

• Stochastic loss reserving models are crucial for financial stability in insurance.
• Micro-level claims data offers granular insights into potential liabilities.
• Previous models did not fully capture the dynamic relationship between catastrophe severity and financial parameters.

Purpose of the Study:

• To extend existing stochastic loss reserving models for incurred but not reported (IBNR) micro-level claims.
• To incorporate catastrophe severity as a measure of event impact.
• To model the interdependency of event timing, severity, and discount rates.

Main Methods:

• Developed a Markovian model where disaster timing and discount rates are dependent on prior event severity.
• Analyzed the moments of IBNR liabilities within this new framework.
• Extended the time horizon for IBNR claims analysis.

Main Results:

• The model quantifies the impact of catastrophe severity on claim liabilities.
• It provides a method to calculate the moments of IBNR liabilities under dynamic conditions.
• The framework allows for a more comprehensive assessment of long-term IBNR liabilities.

Conclusions:

• The proposed model offers a more sophisticated approach to IBNR loss reserving.
• Linking catastrophe severity to financial variables enhances the accuracy of liability estimations.
• This research provides valuable tools for insurers managing complex risks.