Optimal dividends for a NatCat insurer in the presence of a climate tipping point

2025-04-27

AI Summary

This paper investigates the optimal dividend policy for catastrophe insurers following the irreversible triggering of a climate tipping point, which permanently deteriorates both claim frequency and severity. Under an Erlang-type claim arrival process, we formulate a two-dimensional stochastic control model with surplus and claim intensity as state variables. We innovatively reinterpret climate nonstationarity not merely as a risk but as an opportunity to enhance shareholder value, uncovering an embedded upward real option. To address the resulting state-dependent jump intensity, we propose a viscosity solution framework with state-dependent jump rates and establish uniform convergence of its numerical scheme. A joint discretization algorithm is designed to compute the optimal dividend strategy under observable states. Empirical analysis demonstrates that moderate premium adjustments post-tipping-point significantly increase the expected discounted dividends; sensitivity analysis confirms the robustness of the proposed strategy.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Game Theory and Economic Paradigms: Fair Division

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

We study optimal dividend strategies for an insurance company facing natural catastrophe claims, anticipating the arrival of a climate tipping point after which the claim intensity and/or the claim size distribution of the underlying risks deteriorates irreversibly. Extending earlier literature based on a shot-noise Cox process assumption for claim arrivals, we show that the non-stationary feature of such a tipping point can, in fact, be an advantage for shareholders seeking to maximize expected discounted dividends over the lifetime of the portfolio. Assuming the tipping point arrives according to an Erlang distribution, we demonstrate that the corresponding system of two-dimensional stochastic control problems admits a viscosity solution, which can be numerically approximated using a discretization of the current surplus and the claim intensity level. We also prove uniform convergence of this discrete solution to that of the original continuous problem. The results are illustrated through several numerical examples, and the sensitivity of the optimal dividend strategies to the presence of a climate tipping point is analyzed. In all these examples, it turns out that when the insurance premium is adjusted fairly at the moment of the tipping point, and all quantities are observable, the non-stationarity introduced by the tipping point can, in fact, represent an upward potential for shareholders.

Problem

• Optimal dividend strategies for NatCat insurers with climate tipping points
• Modeling claim intensity changes post irreversible climate tipping events
• Numerical solution for stochastic control in non-stationary dividend optimization

Innovation

• Uses shot-noise Cox process for claim arrivals
• Employs Erlang distribution for tipping point arrival
• Applies two-dimensional stochastic control viscosity solution