Gradient catastrophe and flutter in vortex filament dynamics

Gradient catastrophe and flutter instability in the motion of vortex filament within the localized induction approximation are analyzed. It is shown that the origin if this phenomenon is in the gradient catastrophe for the dispersionless Da Rios system which describes motion of filament with slow varying curvature and torsion. Geometrically this catastrophe manifests as a rapid oscillation of a filament curve in a point that resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painlev\'e-I equation.Comment: 11 pages, 3 figures, typos corrected, references adde

The Demand for Homeowners Insurance with Bundled Catastrophe Coverage

This paper analyzes the demand for homeowners insurance in markets subject to catastrophe losses and where consumers have choices in configuring their coverage for catastrophe and non-catastrophe perils. We estimate the demand for homeowner insurance in Florida and New York using two-stage least squares regression with advisory indicated loss costs as our proxy for the quantity of real insurance services demanded. We decompose the demand for insurance into the demand for coverage of catastrophe perils (i.e., hurricanes or windstorms) and the demand for non-catastrophe coverage and estimate these demand functions separately. Our results are relatively consistent in New York and Florida, including evidence that catastrophe demand is more price elastic than non-catastrophe demand. We also find evidence that consumers value options that expand coverage, buy more insurance when it is subsidized through regulatory price constraints, and consider state guaranty fund provisions when purchasing insurance.

Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in markets. We support our methodology by simulations where we also discuss the importance of stochastic noise and volatility in deterministic cusp catastrophe model. The methodology is empirically tested on almost 27 years of U.S. stock market evolution covering several important recessions and crisis periods. Due to the very long sample period we also develop a rolling estimation approach and we find that while in the first half of the period stock markets showed marks of bifurcations, in the second half catastrophe theory was not able to confirm this behavior. Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets

Financial Innovation in Property Catastrophe Reinsurance: The Convergence of Insurance and Capital Markets

The property catastrophe reinsurance industry faces a major challenge. Since 1989, climatic volatility has produced unprecedented insured losses of $43 billion,$18 billion of which were from Hurricane Andrew alone. A surge of insurer defaults and dramatic changes in capacity and pricing have followed in their wake. Catastrophic risks must be addressed with innovative financial approaches that bring the insurance industry closer to the securities industry. This article discusses the new financial instruments that can be successfully used to hedge unknown catastrophe risks.insurance; catastrophe; financial markets; securitization; hedge; climate change; climate volatility; reinsurance; capacity; catastrophic risk; catastrophe bundles; catastrophe futures; law of large numbers; risk financing

Orthogonality catastrophe and Kondo effect in graphene

Anderson's orthogonality catastrophe in graphene, at energies close to the Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality catastrophe is suppressed, due to the vanishing density of states at the Dirac point. In the presence of preexisting localized states at the Dirac energy, the orthogonality catastrophe shows similar features to those found in normal metals with a finite density of states at the Fermi level. The implications for the Kondo effect induced by magnetic impurities, and for the Fermi edge singularities in tunneling processes are also discussed.Comment: 7 pages, 7 figure

Gravothermal Catastrophe, an Example

This work discusses gravothermal catastrophe in astrophysical systems and provides an analytic collapse solution which exhibits many of the catastrophe properties. The system collapses into a trapped surface with outgoing energy radiated to a future boundary, and provides an example of catastrophic collapse.Comment: To appear in Phys. Rev.

Catastrophe risk pricing : an empirical analysis

The price of catastrophe risks is viewed by many to be too high and/or too volatile. Catastrophe risk practitioners point out that, contrary to standard insurance, such as automobile insurance, catastrophe re-insurance is exposed to infrequent but potentially very large losses. It thus requires keeping a large amount of capital in hand, generating a cost of capital to be added to the long-term expected loss. This paper pulls together data from about 250 catastrophe bonds issued on the capital markets to investigate how catastrophe risks are priced. The analysis reveals that catastrophe risk prices are a function of the underlying peril, the expected loss, the wider capital market cycle, and the risk profile of the transaction. The market-based catastrophe risk price is estimated to be 2.69 times the expected loss over the long term, that is, the long-term average multiple is 2.69. When adjusted from the market cycle, the multiple is estimated at 2.33. Peak perils like US Wind are shown to have a much higher multiple than that of non-peak perils like Japan Wind, revealing the diversification of credit from the market.Markets and Market Access,Insurance&Risk Mitigation,Debt Markets,Access to Markets,Emerging Markets