Catastrophe Risk Management in Climate Change

Abstract

Climate change challenges several assumptions underlying the insurability of catastrophe risks. Losses can be heavy-tailed, multiple participants can be exposed to the same systemic climate drivers, and the severity of extreme losses must be assessed from limited and potentially heterogeneous data. These features weaken conventional diversification and make both the design and quantitative assessment of insurance mechanisms more difficult. This thesis develops an integrated framework for managing catastrophe risk under these challenges in three connected steps: (i) diagnosing when risk pooling succeeds or fails, (ii) designing pooling mechanisms when simple pooling is insufficient, and (iii) improving the reliability of these decisions by accounting for uncertainty in the estimation of tail risk.

In Chapter 3, we study the limits of diversification under a general additive heavy-tailed factor model in which each participant’s loss consists of a common systemic component with heterogeneous and potentially random exposure and an idiosyncratic component. We derive participant-level tail and diversification ratios that compare a participant’s risk capital requirement when participating in the pool with the corresponding requirement when standing alone, and characterize conditions for pool viability under different relative tail regimes for the systemic and idiosyncratic factors. The results show that when systemic risk dominates, diversification depends critically on the dependence structure of participants’ exposures. In particular, complementary exposure structures generate greater diversification, while in growing pools the limiting diversification benefit depends jointly on the relative growth of the loss threshold and pool size, and on the concentration of participants’ systemic exposures.

Motivated by the possibility that pooling alone may fail to provide a diversification benefit under heavy-tailed systemic risk, Chapter 4 treats risk pooling as a design problem involving three complementary mechanisms: assessment design, participant selection, and external tail-risk transfer. For a fixed pool, we derive minimax assessment rules that maximize the diversification benefit of the least advantaged participant and characterize pool viability. Then we study optimal pool composition, introducing a diversification index to guide participant selection according to the complementarity of their systemic exposure profiles. Finally, we examine the effect of an insurance-linked securities layer on finite-level diversification. Simulation results demonstrate that combining these mechanisms improves pool viability exposed to heavy-tailed systemic risk.

The implementation of these pooling and design decisions depends critically on the reliable estimation of tail heaviness. However, conventional tail-index estimators can be sensitive to contamination, heterogeneity, threshold selection, and slow convergence to the asymptotic tail model. Therefore, Chapter 5 develops Wasserstein distributionally robust versions of the Hill estimator and a power-based tail-index estimator. The proposed estimators explicitly account for distributional uncertainty around the empirical distribution. Simulation studies show that the distributionally robust estimators reduce downside underestimation under contaminated-mixture distributions and distributions with slow convergence to their asymptotic tails, although this protection may be accompanied by additional conservatism under simple Pareto cases. An application to Norwegian fire insurance claims illustrates how the proposed distributionally robust estimated tail indices and extreme quantiles could be used as conservative, stress-adjusted assessments of extreme-loss risk.

In addition to the quantitative study of physical climate risk in the main chapters, this thesis considers climate liability risk as a complementary dimension of climate risk management. Appendix A examines the measurement and modeling of climate liability risk arising from climate-related litigation, regulatory and disclosure obligations, and evolving standards of corporate responsibility associated with the transition to a low-carbon emission. This complementary study broadens the perspective of the thesis from the management of physical catastrophe losses to the wider range of risks that climate change creates for insurers and other organizations.

The thesis shows that managing heavy-tailed systemic risk requires more than increasing the scale of risk pooling. Effective risk management requires identifying when systemic risk is diversifiable, redesigning pooling arrangements in response to the limits of diversification, and ensuring that these decisions remain reliable under uncertainty about the underlying tail behavior. The thesis thereby connects the diagnosis, design, and estimation problems within a unified framework for catastrophe risk management under climate change.