Paper: arXiv 2401.04378

Authors: Zan Yu, Lianzeng Zhang

Abstract

In this paper, we propose a new efficient method for calculating the Gerber-Shiu discounted penalty function. Generally, the Gerber-Shiu function usually satisfies a class of integro-differential equation. We introduce the physics-informed neural networks (PINN) which embed a differential equation into the loss of the neural network using automatic differentiation. In addition, PINN is more free to set boundary conditions and does not rely on the determination of the initial value. This gives us an idea to calculate more general Gerber-Shiu functions. Numerical examples are provided to illustrate the very good performance of our approximation.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper applies Physics-Informed Neural Networks (PINNs) to solve the integro-differential equations governing the Gerber-Shiu function with dividend barriers and interest. While mathematically sophisticated in combining deep learning with actuarial risk theory, the empirical section relies primarily on synthetic numerical examples rather than real-world market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Compute Gerber-Shiu Function with Interest & Dividend Barrier] --> B[Input: Risk Model Parameters & Initial Conditions]
    B --> C[Formulate Integro-Differential Equation IDE]
    C --> D[Construct Physics-Informed Neural Network PINN]
    D --> E[Embed IDE & Boundary Conditions into Loss via Automatic Differentiation]
    E --> F[Train Neural Network to Minimize Combined Loss]
    F --> G[Outcome: Efficient, Accurate Gerber-Shiu Function Approximation]

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0 of 49 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.