Statistical models are necessary to quantify and understand the risk from natural hazards. A statistical framework is developed here to investigate the e ect of dependence between the frequency and intensity of natural hazards on the aggregate risk. The aggregate risk of a natural hazard is de ned as the sum of the intensities for all events within a season. This framework is applied to a database of extra tropical cyclone tracks from the NCEP-NCAR reanalysis for the October to March extended winters between 1950 and 2003. Large positive correlation is found between cyclone counts and the local mean vorticity over the exit regions of the North Atlantic and North Paci c storm tracks. The aggregate risk is shown to be sensitive to this dependence, especially over Scandinavia. Falsely assuming independence between the frequency and intensity results in large biases in the variance of the aggregate risk. Possible causes for the dependence are investigated by regressing winter cyclone counts and local mean vorticity on teleconnection indices with Poisson and linear models. The indices for the Scandinavian pattern, North Atlantic Oscillation and East Atlantic Pattern are able to account for most of the observed positive correlation over the North Atlantic. The sensitivity of extremes of the aggregate risk distribution to the inclusion of clustering, with and without frequency intensity dependence, is investigated using Cantelli bounds and a copula simulation approach. The inclusion of dependence is shown to be necessary to model the clustering of extreme events. The implication of these ndings for the insurance sector is investigated using the loss component of a catastrophe model. A mixture model approach provides a simple and e ective way to incorporate frequency-intensity dependence into the loss model. Including levels of correlation and overdispersion comparable to that observed in the reanalysis data results in an average increase of over 30% in the 200 year return level for the aggregate loss.

This dissertation thesis address how aggregate shocks affect insurance firms' risk management and asset investment decisions as well as the impact of these decisions on insurance prices and regulation. The first chapter develops a signaling model to examine how insurance firms choose among retention, reinsurance and securitization especially for catastrophe risks. The second chapter examines the determination of insurance prices in an integrated equilibrium framework where insurers' assets may be subject to both idiosyncratic and aggregate shocks. The third chapter presents an empirical analysis of the hypothesized impacts of internal capital and asset risk on insurance prices as predicted by the results of the second chapter. The last chapter investigates the optimal design of insurance regulation to achieve the Pareto optimal asset and liquidity management by insurers as well as risk sharing between insurers and insurees. Chapter 1 provides a novel explanation for the predominance of retention and reinsurance relative to securitization in catastrophe risk transfer using a signaling model. An insurer's risk transfer choice trades off the lower signaling costs of reinsurance against the additional costs of reinsurance stemming from sources such as their market power, higher cost of capital relative to capital markets, and compensation for their monitoring costs. In equilibrium, the lowest risk insurers choose reinsurance, while intermediate and high risk insurance choose partial and full securitization, respectively. An increase in the loss size increases the average risk of insurers who choose securitization. Consequently, catastrophe risks, which are characterized by low frequency-high severity losses, are only securitized by very high risk insurers. Chapter 2 develops a unified equilibrium model of competitive insurance markets where insurers' assets may be exposed to idiosyncratic and aggregate shocks. We endogenize the relationship between insurance prices and insurers internal capital that potentially reconcile the conflicting predictions of previous theories that investigate the relation using partial equilibrium frameworks. Equilibrium effects lead to a non-monotonic U-shaped relation between insurance price and internal capital. Specifically, the equilibrium insurance price first decreases with a positive shock to the internal capital when it is below certain threshold level, and then increases with a positive shock the internal capital when it is above the threshold level. Further, we also derive another testable implication that an increase in the asset default risk increases the insurance price and decrease the insurance coverage. Chapter 3 studies the property and casualty insurance industry in periods from 1992 to 2012 based on the aggregate level of NAIC data. We show that the insurance price decreases with an increase in the surplus of insurance firms at the end of the previous year when the surplus is lower than 8.5 billion, and then increase when the surplus is higher than 8.5 billion. Our results provide support for the hypothesis of a U-shaped relationship between internal capital and insurance price. Our results also provide evidence for the positive relationship between asset portfolio risk and insurance price. Chapter 4 studies the effects of aggregate risk on the Pareto optimal asset and liquidity management by insurers as well as risk-sharing between insurers and insurers. When aggregate risk is low, both insurers and insurers hold no liquidity reserves, insurees are fully insured, and insurers bear all aggregate risk. When aggregate risk takes intermediate values, both insurees and insurers still hold no liquidity reserves, but insurers partially share aggregate risk with insurers. When aggregate risk is high, however, it is optimal to hold nonzero liquidity reserves, and insurees partially share aggregate risk with insurers. The efficient asset and liquidity management policies as well as the aggregate risk allocation can be implemented through a regulatory intervention policy that combines a minimum liquidity requirement when aggregate risk is high, "ex post" contingent on the aggregate state, comprehensive insurance policies, and reinsurance.

I develop a novel method for computing globally accurate solutions to recur- sive macro-epidemic models featuring aggregate uncertainty and a potentially large number of state variables. Compared to the previous literature which either restricts attention to perfect-foresight economies amendable to sequence- space representation or focuses on highly simplified, low dimensional models that could can be analyzed using standard dynamic programming and linear projection techniques, I develop a deep learning-based algorithm that can han- dle rich environments featuring both aggregate uncertainty and large numbers of state variables. In addition to solving for particular model equilibria, I show how the deep learning method could be extended to solve for a whole set of models, indexed by the parameters of government policy. By pre-computing the whole equilibrium set, my deep learning method greatly simplifies compu- tation of optimal policies, since it bypasses the need to re-solve the model for many different values of policy parameters. 1

Yes / Drawing on distinct German institutional characteristics related to cultural, legal, financial, and regulatory features, this paper investigates the extent to which environmental incentives influence German non-financial firms in revealing risk information in their annual report narratives. The paper also examines whether risk-related disclosure (aggregate risk reporting and the tone of news about risk) is useful by investigating its impact on market liquidity and investor-perceived risk. We find that the decision to provide or withhold such risk information is less likely to be significantly associated with environmental incentives. Among those incentives, we find that German firms are significantly influenced by their underlying risks rather than other factors including ownership structure, capital structure, external equity finance, and borrowing. The decision to disclose is likely to be influenced by the size of the firm and whether or not it produces lengthy annual reports. The results also suggest that the impact of aggregate risk reporting levels was not observable until a distinction was made between bad and good news about risk. Specifically, we find that the German market tends to positively (negatively) price good (bad) news about risk by either improving (worsening) market liquidity through removing (creating) information asymmetries, or reducing (increasing) investor-perceived risk.