Asymptotics of Ruin Probabilities in a Subordinated Cramér-Lundberg Model

Battle Count: 91

This paper is primarily relevant to insurance risk management and actuarial science rather than quantitative trading. However, the mathematical tools (Lévy processes, subordination, heavy-tailed distributions, stochastic dominance) are shared with quantitative finance. The findings on how clustering transforms light-tailed to heavy-tailed distributions could inform tail risk modeling in trading contexts. The connection to Nat-Cat and catastrophe bonds provides a bridge to structured finance products.

The theoretical framework requires deep knowledge of Lévy process theory, subordination, regular variation, and ruin theory. Implementing the model computationally would require: (1) simulation of Lévy subordinators with specified Lévy measures; (2) computation of Laplace exponents and their inverses; (3) numerical evaluation of adjustment coefficients; (4) handling of regularly varying tails for asymptotic calculations. The mathematical proofs are complex but the computational implementation for specific examples (like Example 1) is straightforward.

This is a purely theoretical paper with complete mathematical proofs. All theorems, lemmas, and corollaries are fully proved within the paper. The mathematical derivations are self-contained and verifiable. However, there is no computational code or numerical experiments to reproduce. The examples (Example 1, Example 2) are analytically tractable and can be verified by hand.