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

2025-04-23

AI Summary

This study addresses the catastrophe excess-of-loss reinsurance contract optimization problem, jointly determining the attachment point, limit, and reinstatement terms to maximize expected profit while satisfying risk measures (e.g., VaR, CVaR) and regulatory capital constraints. We propose a hybrid optimization framework integrating simulated annealing’s local search capability with a quantum-inspired branch-and-bound structure, augmented by application-driven compact bounding techniques that significantly improve the efficiency of generating high-quality contracts under multiple constraints. Our method demonstrates the robustness of classical algorithms in optimizing complex reinsurance structures. Furthermore, through quantum feasibility analysis and boundary sensitivity studies, we identify the hardware requirements for quantum acceleration and delineate key pathways for algorithmic improvement—thereby establishing both theoretical foundations and architectural blueprints for future quantum-classical hybrid solvers in actuarial optimization.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Agentic search

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.

Problem

• Optimize reinsurance contracts using modern computational methods
• Maximize profit while considering risk and regulatory constraints
• Explore quantum computing potential for future optimization speedup

Innovation

• Simulated annealing for local search optimization
• Quantum branch & bound for future speedup
• Robust framework handling realistic constraints