price reinsurance instruments

This study addresses the critical limitation of traditional catastrophe risk pricing models, which ignore the non-stationarity in disaster frequency induced by climate change, leading to biased reinsurance and catastrophe bond valuations and a systematic underestimation of capital reserves. To rectify this, the authors propose a climate-aware pricing framework that, for the first time, incorporates a temperature-driven stochastic intensity into a Cox process: the catastrophe arrival intensity depends on a temperature index modeled by an Ornstein–Uhlenbeck process with a time trend, coupled with a compound Poisson loss structure. Valuation is performed under a risk-adjusted measure via Monte Carlo simulation. Empirical results demonstrate that the model significantly increases excess-of-loss reinsurance premiums and reduces catastrophe bond prices; compared to a stationary benchmark, the 99.5% TVaR reveals that economic capital requirements are underestimated by approximately 13.7%, underscoring the essential role of integrating climate dynamics into risk management.

Under heavy-tailed loss distributions—such as those arising from extreme weather events—the expected loss may be infinite, rendering conventional indemnity-based insurance inadequate for risk transfer. Method: This paper proposes a hybrid insurance mechanism integrating traditional capped indemnity insurance (front-end) with index-based parametric insurance (back-end) for excess losses. We develop a novel optimization criterion specifically tailored to Pareto-type extreme-value distributions and rigorously establish its convergence under heavy-tailed conditions. The framework combines extreme value theory (EVT) modeling, Monte Carlo simulation, and empirical calibration using U.S. tornado loss data. Contribution/Results: The calibrated hybrid contract significantly outperforms conventional capped indemnity contracts in both protection efficacy and cost efficiency. Notably, it enhances payout speed, accuracy, and robustness under extreme-loss scenarios—demonstrating superior risk-transfer performance while maintaining actuarial feasibility.

This paper addresses the inadequate modeling of multiregional loss dependence structures in cross-regional catastrophe (CAT) bond pricing. We develop a unified multi-regional pricing framework that systematically characterizes independent, proportional, and general bivariate extreme-value dependence structures, and integrates the Wang transform to explicitly incorporate market risk preferences. Using historical PCS loss data, we empirically assess how alternative dependence assumptions affect CAT bond prices and derive a closed-form normal approximation solution. Results demonstrate that the choice of dependence structure significantly impacts pricing outcomes, while the normal approximation maintains high accuracy under real-world data. This study provides a theoretically consistent, computationally efficient, and operationally practical valuation tool for the design and risk management of multi-regional CAT bonds.

This paper addresses the challenge of predicting loss ratios for unissued policy pools and modeling loss development across future accident years in casualty insurance-linked securities (ILS). We propose the first end-to-end Bayesian workflow for this problem. Methodologically, we integrate theory-driven state-space and time-series models with industry-informed priors, model stacking, and simulation-based calibration—leveraging Schedule P data for both prior predictive checks and posterior validation. Compared to conventional approaches, our framework significantly improves accuracy and interpretability in modeling long-term loss uncertainty. Comprehensive multi-model benchmarking demonstrates robust predictive performance across diverse scenarios. The methodology delivers actionable, quantitatively rigorous support for pricing and risk transfer in casualty ILS markets.

This paper addresses the challenge of quantifying business impact from predictive model improvements in insurance pricing. We establish, for the first time, an analytical relationship between model performance and loss ratio. A novel metric—Loss Ratio Error (LRE)—is introduced, linking prediction accuracy to actual financial loss via Pearson correlation, thereby enabling quantitative mapping from model-level metrics (e.g., RMSE) to business-level KPIs. We develop a unified analytical framework integrating frequency, severity, and pure premium models, combining closed-form derivations with Monte Carlo simulation to achieve high-accuracy loss ratio estimation under realistic assumptions; model performance degrades gracefully under assumption shifts, ensuring decision robustness. Our key contribution is the formal identification of diminishing marginal returns in model optimization: incremental accuracy gains yield progressively smaller reductions in loss ratio. This insight shifts pricing model evaluation from heuristic judgment toward cost-benefit-driven, quantitative decision-making.

This study addresses the high computational cost of asset-liability management (ALM) models in the insurance industry, particularly in large-scale sensitivity analyses and stress testing for solvency capital assessment and asset allocation optimization. It introduces path signature theory into ALM modeling for the first time, approximating key outputs—such as embedded value and best estimate—as linear combinations of path signatures derived from economic scenario trajectories. A regularized linear regression framework is then employed to construct a surrogate model. This approach substantially reduces computational overhead while maintaining high predictive accuracy and demonstrating robustness to shifts in the underlying economic scenario distribution, thereby enabling efficient large-scale balance sheet evaluation and rapid decision support.