Based on a previous study by Amador and Weill (2009), I study the diffusion of dispersed private information in a large economy subject to a ”catastrophe risk” state. I assume that agents learn from the actions of oth- ers through two channels: a public channel, that represents learning from prices, and a bi-dimensional private channel that represents learning from lo- cal interactions via information concerning the good state and the catastrophe probability. I show an equilibrium solution based on conditional Bayes rule, which weakens the usual condition of ”slow learning” as presented in Amador and Weill and first introduced by Vives (1993). I study asymptotic conver- gence ”to the truth” deriving that ”catastrophe risk” can lead to ”non-linear” adjustments that could in principle explain fluctuations of price aggregates. I finally discuss robustness issues and potential applications of this work to models of ”reaching consensus”, ”investments under uncertainty”, ”market efficiency” and ”prediction markets”. / text

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.

In this thesis we will elaborate on multivariate extreme value modelling, re- lated practical and theoretical aspects. We will mainly focus on the dependence models, the extreme value copulas in particular. Extreme value copulas effec- tively unify the univariate extreme value theory and the copula framework itself in a single view. We familiarize ourselves with both of them in the first two chapters. Those chapters present generalized extreme value distribution, gen- eralized Pareto distribution and Archimedean copulas, that are suitable for the multivariate maxima and the threshold exceedances description. These two top- ics will be addressed in the third chapter in detail. Taking into consideration rather practical focus of this thesis, we examine the methods of data analysis extensively. Furthermore, we will employ these methods in a comprehensive case study, that will aim to reveal the importance of extreme value theory application in the Catastrophe Insurance. 1

台灣由於特殊的地理位置，所以地震、颱風等巨災所造成之損失時有所聞。這些巨災除造成交通、農業等經濟損失，更造成人員傷亡、房屋倒塌，也在每個人心中都刻畫難以抹滅的傷痛。為了因應這些巨災帶來的損失，台灣政府撥出許多補助費用予死傷及失蹤人民或其家屬，也提供某些房屋損失的補助。巨災不只危害個人，也同樣衝擊政府財政。 本文以台灣的地震風險為研究對象，並將地震損失劃分為經濟損失與財政損失。經濟損失泛指因地震所造成之一切直接損失，財政損失係指政府因災後所需之賑災與重建經費。因此本文不僅考慮地震所帶來的直接損失，同時也涵蓋政府對於災後的各項補助措施，以完整描述地震全面性的影響範圍。除描述地震整體影響外，本文另設計三種政府預算保險（比例式、自負額、給付最高額度與自負額並行等）作為風險管理機制。模擬說明有無風險管理機制輔助之下對地震損失所帶來之影響及其差異，可從中分析此保險的成本和效益。 本文主要使用國家地震工程研究中心提供之一般建築物損失資料表，輔以中央政府各主管機關對於其下轄業務範圍內之損失統計年報，從中取得因地震所造成之損失統計資料，例如傷亡與失蹤人數、房屋倒塌數、交通損失以及農業損失等，來建立損失模型。損失模型之建立係以模擬出之一般建築物損失為基礎，用迴歸分析評估其與其他損失之相關性，再建立其他損失模型。 本文之分析說明政府若能落實巨災風險管理，將產生極大的利益，在減少社會經濟損失方面尤為顯著。巨災風險管理是正面且必要之事，無論是住宅地震保險基金或政府預算保險，依初始規劃角度來看，政府皆扮演風險管理者的角色。 / Taiwan is usually hit and hurt by some natural catastrophes several times in a year due to its special location. Natural catastrophes brought not only losses of personal properties, agricultural products, and infrastructures but also casualties that brought painful, lasting feelings. In order to deal with the losses caused by natural catastrophes, Taiwan government released significant amount of consolation money for the dead, missing, and injured people. The government also compensate for some house losses. Catastrophes affect not only the private sector economy but also the public finance. This paper focuses on the impacts of the earthquake risk on economic losses and public finance losses of Taiwan. The economic losses include all reported losses while the public finance losses reflect the expenses paid for the post-disaster need, including disaster relief and reconstruction. Considering both the economic losses and public finance losses give us a better-informed picture about the consequences of natural catastrophes. After establishing the models for various types of losses, we analyze how government budget insurances can mitigate the natural catastrophe risks. We employ simulations to display the differences in the loss distributions with and without the insurance. The costs and benefits of the insurance can then be analyzed. Our model of the earthquake risk is based upon the scenario output generated by a model of the National Center for Research on Earthquake Engineering of Taiwan. We coupled the scenarios and official statistics on the earthquake losses to construct the building loss model. The models for other types of losses are then established using regression analyses. The above analyses demonstrate how the risk management on natural catastrophes taken by the government can benefit Taiwan. The benefits on the economic losses of the society are particularly apparent. Catastrophe risk management is positive and necessary. The Taiwan Residential Earthquake Insurance Fund and government budget insurance are the measures for the risk manager - the government.

When society fails to effectively integrate natural and constructed environments, one of the cataclysmic byproducts of this disconnect is an increased risk of natural disasters. On top of the devastation that is the aftermath of such disasters, poor planning and engineering decisions have detrimental effects on communities as they attempt to recover and rebuild. While there is an inherent difficulty in the quantification of the cost of human life, interruption in business operations, and damage to the properties, it is critical to develop plans and mitigation strategies to promote fast recovery. Traditionally insurance and reinsurance products have been used as a mitigation strategy for financing post-disaster recovery. However, there are number of problems associated with these models such as lack of liquidity, defaults, long litigation process, etc. In light of these problems, new Alternative Risk Transfer (ART) methods are introduced. The pricing of these risk mitigating instruments, however, has been mostly associated with the hazard frequency and intensity; and little recognition is made of the riskiness of the structure to be indemnified. This study proposes valuation models for catastrophe-linked ART products and insurance contracts in which the risks and value can be linked to the characteristics of the insured portfolio of constructed assets. The results show that the supply side ? structural parameters are as important as the demand ? hazard frequency, and are in a highly nonlinear relationship with financial parameters such as risk premiums and spreads.

運用傳統再保險契約移轉風險受限於承保能量的逐年波動，尤其自90年代起，全球巨災頻繁，保險人損失巨幅增加，承保能量急遽萎縮，基於巨災市場之資金需求，再保險轉向資本市場，預期將巨災風險移轉至投資人，促成保險衍生性金融商品之創新，本研究針對佔有顯著交易量的巨災風險債券進行分析，基於Cummins和Geman (1995)所建構巨災累積損失模型，引用Duffie 與Singleton (1999)於違約債券的計價模式，將折現利率表示為短期利率加上事故發生率及預期損失比例之乘積，並將債券期間延長至多年期，以符合市場承保的需求，應用市場無套利假設及平賭測度計價的方法計算合理的市場價值，巨災損失過程將分成損失發展期與損失確定期，以卜瓦松過程表示巨災發生頻率，並利用台灣巨災經驗資料建立合適之損失幅度模型，最後以蒙地卡羅方法針對三種不同型態的巨災風險債券試算合理價值，並具體結論所得的數值結果與後續之研究建議。 / Using traditional reinsurance treaties to transfer insurance risks are restrained due to the volatility of the underwriting capacity annually. Catastrophe risks have substantially increased since the early 1990s and have directly resulted significant claim losses for the insurers. Hence the insurers are pursuing the financial capacities from the capital market. Transferring the catastrophe risks to the investor have stimulated the financial innovation for the insurance industry. In this study, pricing issues for the heavily traded catastrophe risk bonds (CAT-bond) are investigated. The aggregated catastrophe loss model in Cummins and Geman (1995) are adopted. While the financial techniques in valuing the defaultable bonds in Duffie and Singleton (1999) are employed to determine the fair prices incorporating the claim hazard rates and the loss severity. The duration of the CAT-bonds is extended from single year to multiple years in order to meet the demand from the reinsurance market. Non- arbitrage theory and martingale measures are employed to determine their fair market values. The contract term of the CAT-bonds is divided into the loss period and the development period. The frequency of the catastrophe risk is modeled through the Poisson process. Taiwan catastrophe loss experiences are examined to build the plausible loss severity model. Three distant types of CAT-bonds are analyzed through Monte Carlo method for illustrations. This paper concludes with remarks regarding some pricing issues of CAT-bonds.