Paper: arXiv 2603.01821

Authors: Jonathan Klinge, Maren Diane Schmeck

Abstract

We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events, this process is time-changed by a Lévy subordinator. The subordinator is chosen so that it evolves, on average, at the same speed as calendar time, creating a trade-off between intensity and severity. We show that such a transformation always has a negative impact on the probability of ruin. Despite the expected total claim amount remaining invariant, it turns out that the probability of ruin as a function of the initial capital falls arbitrarily slowly depending on the choice of the subordinator.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a strong, mathematically rigorous framework applying Lévy subordinators to the classic Cramér-Lundberg model to quantify catastrophic loss clustering and ruin probability asymptotics. However, it is purely theoretical with no empirical datasets, real-world calibrations, or numerical simulations included in the excerpt.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess Impact of Claim Clustering via Time Change on Ruin Probability] --> B[Input: Base Compound Poisson Process + Lévy Subordinator]
    B --> C[Method: Apply Subordinator to CP Process via Time Change]
    C --> D[Constraint: Match Subordinator Average Speed to Calendar Time]
    D --> E[Analysis: Compute Asymptotics of Ruin Probability vs Initial Capital]
    E --> F[Outcome 1: Total Expected Claim Amount Remains Invariant]
    E --> G[Outcome 2: Time Change Always Increases Ruin Probability]
    E --> H[Outcome 3: Ruin Probability Falls Arbitrarily Slowly Based on Subordinator]

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