Paper: arXiv 2410.14985

Authors: Andrew Fleck, Edward Furman, Yang Shen

Abstract

Nowadays insurers have to account for potentially complex dependence between risks. In the field of loss reserving, there are many parametric and non-parametric models attempting to capture dependence between business lines. One common approach has been to use additive background risk models (ABRMs) which provide rich and interpretable dependence structures via a common shock model. Unfortunately, ABRMs are often restrictive. Models that capture necessary features may have impractical to estimate parameters. For example models without a closed-form likelihood function for lack of a probability density function (e.g. some Tweedie, Stable Distributions, etc). We apply a modification of the continuous generalised method of moments (CGMM) of [Carrasco and Florens, 2000] which delivers comparable estimators to the MLE to loss reserving. We examine models such as the one proposed by [Avanzi et al., 2016] and a related but novel one derived from the stable family of distributions. Our CGMM method of estimation provides conventional non-Bayesian estimates in the case where MLEs are impractical.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper tackles a technically challenging actuarial problem by applying Continuous Generalised Method of Moments (CGMM) to Additive Background Risk Models (ABRMs) with heavy-tailed, non-closed-form distributions like Stable and Tweedie. It demonstrates solid mathematical rigor and practical computational benefits over standard MLE, though empirical evaluation relies primarily on synthetic simulation triangles.

Research Flowchart

  flowchart TD
    A["Research Goal: Estimate complex dependence in loss reserving when MLE is impractical"] --> B["Input: Loss Reserving Models with Additive Background Risk (ABRM) & Non-Closed Form Likelihoods"]
    B --> C["Model Selection: Avanzi et al. (2016) & Novel Stable Distribution Models"]
    C --> D["Methodology: Modified Continuous Generalized Method of Moments (CGMM)"]
    D --> E["Computational Estimation: Optimize via Characteristic Functions without explicit PDFs"]
    E --> F["Outcome: Practical non-Bayesian estimates with performance comparable to MLE"]

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