Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance

Area of Science:

• Mathematics
• Statistics
• Financial Risk Management

Background:

• Insurance companies often face incomplete knowledge of underlying correlation matrices.
• Accurate correlation matrices are crucial for meeting capital requirements and risk management.

Purpose of the Study:

• To derive explicit solutions for completing partially specified correlation matrices.
• To identify a maximal determinant completion suitable for insurance applications.

Main Methods:

• Derivation of explicit formulae for correlation matrix completion.
• Focus on block structures relevant to insurance and risk management.
• Selection of the maximal determinant completion method.

Main Results:

• Explicit solutions for completing partially specified correlation matrices are provided.
• The maximal determinant completion is identified as suitable for insurance applications.
• The derived formulae simplify practical problem-solving.

Conclusions:

• The study offers practical tools for correlation matrix completion in finance.
• Maximal determinant completion is a valuable approach for insurance risk management.
• The explicit formulae can serve as benchmarks for other algorithms.