Data and uncertainty in extreme risks - a nonlinear expectations approach

Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a heavy-tailed context (in particular when our data are described by a Pareto distribution, as is common in much of extreme value theory), the theory of [5] is insufficient, and requires an additional regularization step which we introduce. By asking whether this regularization is possible, we obtain a qualitative requirement for reliable estimation of tail quantities and risk measures, in a Pareto setting

Sound the Alarm: Limitations of Liability in Alarm Service Contracts

Home and business owners increasingly rely on alarm systems to protect against theft and property damage. When a burglary or fire occurs and an alarm service customer discovers that the alarm company negligently failed to call the police or fire department, the customer understandably would expect redress for the company’s failure to provide its service. Many customers would be surprised, though, to discover that an alarm company’s liability is often contractually limited to a relatively token amount unrelated to the cost of the service, even when the alarm company is negligent. Some states view these limitations of liability as exculpatory clauses and determine their enforceability based on whether they are unconscionable or violate public policy. Other states view them as liquidated damages and apply a penalty test to determine their enforceability. This Note addresses the differences between these two approaches in the context of the unique remedy difficulties inherent in alarm service contracts. This Note then argues that the prevailing policy rationales for enforcing alarm service provisions that limit a party’s liability for its own negligence are misguided and advocates that these provisions should not be enforced as a matter of public policy

Representing filtration consistent nonlinear expectations as gg-expectations in general probability spaces

We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous drivers, where both the martingale and the driver terms are permitted to jump, and the martingale representation is infinite dimensional. To establish this result, we show that this domination condition is sufficient to guarantee that the comparison theorem for BSDEs will hold, and we generalise the nonlinear Doob-Meyer decomposition of Peng to a general context

Chandra detection of extended X-ray emission from the recurrent nova RS Ophiuchi

Radio, infrared, and optical observations of the 2006 eruption of the symbiotic recurrent nova RS Ophiuchi (RS Oph) showed that the explosion produced non-spherical ejecta. Some of this ejected material was in the form of bipolar jets to the east and west of the central source. Here we describe Xray observations taken with the Chandra X-ray Observatory one and a half years after the beginning of the outburst that reveal narrow, extended structure with a position angle of approximately 300 degrees (east of north). Although the orientation of the extended feature in the X-ray image is consistent with the readout direction of the CCD detector, extensive testing suggests that the feature is not an artifact. Assuming it is not an instrumental effect, the extended X-ray structure shows hot plasma stretching more than 1,900 AU from the central binary (taking a distance of 1.6 kpc). The X-ray emission is elongated in the northwest direction - in line with the extended infrared emission and some minor features in the published radio image. It is less consistent with the orientation of the radio jets and the main bipolar optical structure. Most of the photons in the extended X-ray structure have energies of less than 0.8 keV. If the extended X-ray feature was produced when the nova explosion occurred, then its 1".2 length as of 2007 August implies that it expanded at an average rate of more than 2 mas/d, which corresponds to a flow speed of greater than 6,000 km/s (d/1.6 kpc) in the plane of the sky. This expansion rate is similar to the earliest measured expansion rates for the radio jets.Comment: accepted in Ap