Paper: arXiv 2601.07637

Authors: Benjamin Avanzi, Ronald Richman, Bernard Wong, Mario Wüthrich, Yagebu Xie

Abstract

Outstanding claim liabilities are revised repeatedly as claims develop, yet most modern reserving models are trained as one-shot predictors and typically learn only from settled claims. We formulate individual claims reserving as a claim-level Markov decision process in which an agent sequentially updates outstanding claim liability (OCL) estimates over development, using continuous actions and a reward design that balances accuracy with stable reserve revisions. A key advantage of this reinforcement learning (RL) approach is that it can learn from all observed claim trajectories, including claims that remain open at valuation, thereby avoiding the reduced sample size and selection effects inherent in supervised methods trained on ultimate outcomes only. We also introduce practical components needed for actuarial use – initialisation of new claims, temporally consistent tuning via a rolling-settlement scheme, and an importance-weighting mechanism to mitigate portfolio-level underestimation driven by the rarity of large claims. On CAS and SPLICE synthetic general insurance datasets, the proposed Soft Actor-Critic implementation delivers competitive claim-level accuracy and strong aggregate OCL performance, particularly for the immature claim segments that drive most of the liability.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel approach to micro-level actuarial claims reserving by framing it as a continuous-action Markov Decision Process solved with Soft Actor-Critic (SAC). The empirical evaluation is rigorous, utilizing both realistic CAS benchmarks and synthetic SPLICE simulations with extensive benchmarking against standard actuarial methods.

Research Flowchart

  flowchart TD
    A[Research Goal: Dynamic Individual Claims Reserving via Reinforcement Learning] --> B[Data Inputs: Synthetic Datasets CAS & SPLICE]
    B --> C[Methodology: Formulate Claim-Level MDP with Continuous Actions & Rewards]
    C --> D[Computational Engine: Train Soft Actor-Critic RL Agent on Open & Settled Trajectories]
    D --> E[Actuarial Adaptations: Initialisation, Rolling Tuning & Importance Weighting]
    E --> F[Outcomes: Improved OCL Accuracy & Stable Revisions, Especially for Immature Claims]