Modern Computational Methods in Reinsurance Optimization: From Simulated Annealing to Quantum Branch & Bound

Paper: arXiv 2504.16530

Authors: George Woodman, Ruben S. Andrist, Thomas Häner, Damian S. Steiger, Martin J. A. Schuetz, Helmut G. Katzgraber, Marcin Detyniecki

Abstract

We propose and implement modern computational methods to enhance catastrophe excess-of-loss reinsurance contracts in practice. The underlying optimization problem involves attachment points, limits, and reinstatement clauses, and the objective is to maximize the expected profit while considering risk measures and regulatory constraints. We study the problem formulation, paving the way for practitioners, for two very different approaches: A local search optimizer using simulated annealing, which handles realistic constraints, and a branch & bound approach exploring the potential of a future speedup via quantum branch & bound. On the one hand, local search effectively generates contract structures within several constraints, proving useful for complex treaties that have multiple local optima. On the other hand, although our branch & bound formulation only confirms that solving the full problem with a future quantum computer would require a stronger, less expensive bound and substantial hardware improvements, we believe that the designed application-specific bound is sufficiently strong to serve as a basis for further works. Concisely, we provide insurance practitioners with a robust numerical framework for contract optimization that handles realistic constraints today, as well as an outlook and initial steps towards an approach which could leverage quantum computers in the future.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced optimization algorithms like simulated annealing and branch & bound, with detailed mathematical formulation of reinsurance structures and risk measures, but the empirical validation relies on simulated data and conceptual implementation rather than extensive backtesting with real-world datasets.

Research Flowchart

  flowchart TD
  A["Research Goal: Enhance Catastrophe Excess-of-Loss<br>Reinsurance Contracts via Optimization"] --> B["Formulate Optimization Problem<br>Attachment, Limits, Reinstatements, Constraints"]
  B --> C{"Define Two Methodologies"}
  C --> D["Simulated Annealing<br>Local Search Optimizer"]
  C --> E["Quantum Branch & Bound<br>Exploratory Framework"]
  D --> F["Computational Process: Simulate & Iterate<br>Handles Constraints & Local Optima"]
  E --> G["Computational Process: Bound & Prune<br>Validates Future Quantum Feasibility"]
  F --> H["Outcome: Robust Practical Framework<br>Optimizes Contracts Today"]
  G --> I["Outcome: Stronger Bounds Identified<br>Basis for Future Quantum Work"]
  H & I --> J["Final Outcome: Integrated Approach<br>Immediate Practical Value + Future Outlook"]

Cited References (45)

1. Reinsurance: Actuarial and Statistical Aspects (2017) — link
2. An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance (1960)
3. Uncertainty and the welfare economics of medical care. (1963)
4. Risk measures and comonotonicity: A review ({2006})
5. Optimal reinsurance designs based on risk measures: a review (2020) — link
6. Optimal Reinsurance Arrangements Under Tail Risk Measures (2009) — link
7. Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures (2007) — link
8. Optimal Reinsurance under VaR and CVaR Risk Measures: A Simplified Approach (2011)

0 of 45 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.