Approximation of the ruin probability using the scaled Laplace transform inversion

Area of Science:

• Actuarial Science
• Probability Theory
• Numerical Analysis

Background:

• The classical risk model is fundamental in actuarial science for assessing financial stability.
• Calculating the ruin probability, especially for large initial surplus values, presents significant computational challenges.
• Existing methods often rely on Laplace transform inversion, which can be complex to evaluate.

Purpose of the Study:

• To develop and evaluate novel approximations for the ruin probability in the classical risk model.
• To address the challenge of computing ruin probabilities for large initial surplus processes.
• To compare the performance of the proposed approximations against established numerical methods.

Main Methods:

• The study focuses on scaled Laplace transform inversion techniques.
• Approximations are developed to overcome limitations in evaluating the ruin probability at large values.
• A simulation study is conducted to compare the proposed method with existing algorithms.

Main Results:

• The proposed method effectively overcomes the difficulty of evaluating ruin probabilities for large initial surplus values.
• Comparisons demonstrate the efficacy of the new approximations.
• Performance is evaluated against Laplace transform inversions using fixed Talbot, Trefethen-Weideman-Schmelzer, and maximum entropy methods.

Conclusions:

• The developed approximations offer a viable and improved approach to calculating ruin probabilities in risk management.
• The findings are particularly relevant for scenarios with substantial initial capital.
• The study contributes to more robust financial risk assessment in insurance.