Paper: arXiv 2409.09091

Authors: Filip Lindskog, Mario V. Wüthrich

Abstract

Random delays between the occurrence of accident events and the corresponding reporting times of insurance claims is a standard feature of insurance data. The time lag between the reporting and the processing of a claim depends on whether the claim can be processed without delay as it arrives or whether it remains unprocessed for some time because of temporarily insufficient processing capacity that is shared between all incoming claims. We aim to explain and analyze the nature of processing delays and build-up of backlogs. We show how to select processing capacity optimally in order to minimize claims costs, taking delay-adjusted costs and fixed costs for claims settlement capacity into account. Theoretical results are combined with a large-scale numerical study that demonstrates practical usefulness of our proposal.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper uniquely bridges actuarial science and queueing theory by modeling insurance claim backlog processes under capacity constraints. The methodology is rigorously grounded in stochastic processes (Lindley recursions) and enhanced with modern deep learning (RNNs) for high-dimensional approximation and cost optimization.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimize claims capacity to minimize delay-adjusted and fixed costs] --> B[Data Inputs: Accident-to-reporting lags & claim arrival rates]
    B --> C[Methodology: Queueing theory & backlog modeling for shared capacity]
    C --> D[Computational Optimization: Balance delay costs vs. capacity maintenance costs]
    D --> E[Outcomes: Optimal processing capacity selection & capacity constraint insights]