A Hybrid Framework for Reinsurance Optimization: Integrating Generative Models and Reinforcement Learning

Reinsurance optimization is a cornerstone of solvency and capital management, yet traditional approaches often rely on restrictive distributional assumptions and static program designs. We propose a hybrid framework that combines Variational Autoencoders (VAEs) to learn joint distributions of multi-line and multi-year claims data with Proximal Policy Optimization (PPO) reinforcement learning to adapt treaty parameters dynamically. The framework explicitly targets expected surplus under capital and ruin-probability constraints, bridging statistical modeling with sequential decision-making. Using simulated and stress-test scenarios, including pandemic-type and catastrophe-type shocks, we show that the hybrid method produces more resilient outcomes than classical proportional and stop-loss benchmarks, delivering higher surpluses and lower tail risk. Our findings highlight the usefulness of generative models for capturing cross-line dependencies and demonstrate the feasibility of RL-based dynamic structuring in practical reinsurance settings. Contributions include (i) clarifying optimization goals in reinsurance RL, (ii) defending generative modeling relative to parametric fits, and (iii) benchmarking against established methods. This work illustrates how hybrid AI techniques can address modern challenges of portfolio diversification, catastrophe risk, and adaptive capital allocation.

💡 Research Summary

The paper introduces a novel hybrid framework that brings together two state‑of‑the‑art AI techniques—Variational Autoencoders (VAEs) and Proximal Policy Optimization (PPO) reinforcement learning—to tackle the long‑standing problem of reinsurance treaty design under uncertainty. Traditional actuarial approaches typically assume simple parametric claim distributions (e.g., log‑normal or Pareto) and rely on static treaty structures, which limits their ability to capture multi‑line dependencies, tail‑risk dynamics, and evolving regulatory or market conditions.

In the first stage, a VAE is trained on multi‑line, multi‑year claim data. The encoder compresses high‑dimensional loss vectors into a low‑dimensional latent space, while the decoder learns to reconstruct the original data. After training, the decoder can generate a large number of synthetic claim scenarios that preserve the empirical correlation structure and heavy‑tail behavior observed in the real data. This generative step mitigates data scarcity, especially for rare catastrophic events such as pandemics or natural disasters, and provides a richer stochastic environment for downstream optimization.

The second stage embeds a PPO agent in the simulated environment produced by the VAE. At each decision epoch the agent observes a state vector comprising the current surplus, recent claim history, existing treaty parameters (retention rates, attachment and detachment points for each layer), and exogenous risk indicators. The action space is continuous and consists of adjustments to (i) layer‑wise retention rates (δ_k), (ii) attachment points (Δa_k), and (iii) detachment points (Δb_k). The reward function is a weighted sum of three components: (a) expected surplus growth, (b) a penalty for exceeding a solvency‑related ruin probability or VaR threshold, and (c) the cost of reinsurance premiums. By maximizing the expected cumulative reward over a finite planning horizon, the PPO algorithm learns a policy that dynamically re‑balances risk transfer in response to realized claims and market signals.

Mathematically, the surplus process follows a discrete‑time Cramér‑Lundberg recursion extended to incorporate dynamic treaty adjustments. Claims arrive as a Poisson process with intensity λ, and individual claim sizes are i.i.d. The retained loss for each claim is a piecewise linear function of the current treaty parameters, allowing both proportional and layered structures to be represented. The policy optimization problem is expressed as

 max_θ E_{π_θ}