Risk Minimization and Optimal Derivative Design in a Principal Agent Game

We consider the problem of Adverse Selection and optimal derivative design within a Principal-Agent framework. The principal's income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She evaluates her risk using a coherent and law invariant risk measure and tries minimize her exposure by selling derivative securities on her income to individual agents. The agents have mean-variance preferences with heterogeneous risk aversion coefficients. An agent's degree of risk aversion is private information and hidden to the principal who only knows the overall distribution. We show that the principal's risk minimization problem has a solution and illustrate the effects of risk transfer on her income by means of two specific examples. Our model extends earlier work of Barrieu and El Karoui (2005) and Carlier, Ekeland and Touzi (2007).Comment: 28 pages, 4 figure

SGR J1550–5418 Bursts Detected with the Fermi Gamma-Ray Burst Monitor during its Most Prolific Activity

We have performed detailed temporal and time-integrated spectral analysis of 286 bursts from SGR J1550–5418 detected with the Fermi Gamma-ray Burst Monitor (GBM) in 2009 January, resulting in the largest uniform sample of temporal and spectral properties of SGR J1550–5418 bursts. We have used the combination of broadband and high time-resolution data provided with GBM to perform statistical studies for the source properties. We determine the durations, emission times, duty cycles, and rise times for all bursts, and find that they are typical of SGR bursts. We explore various models in our spectral analysis, and conclude that the spectra of SGR J1550–5418 bursts in the 8-200 keV band are equally well described by optically thin thermal bremsstrahlung (OTTB), a power law (PL) with an exponential cutoff (Comptonized model), and two blackbody (BB) functions (BB+BB). In the spectral fits with the Comptonized model, we find a mean PL index of –0.92, close to the OTTB index of –1. We show that there is an anti-correlation between the Comptonized E_(peak) and the burst fluence and average flux. For the BB+BB fits, we find that the fluences and emission areas of the two BB functions are correlated. The low-temperature BB has an emission area comparable to the neutron star surface area, independent of the temperature, while the high-temperature BB has a much smaller area and shows an anti-correlation between emission area and temperature. We compare the properties of these bursts with bursts observed from other SGR sources during extreme activations, and discuss the implications of our results in the context of magnetar burst models

Elliptic Flow Analysis at RHIC: Fluctuations vs. Non-Flow Effects

The cumulant method is applied to study elliptic flow ($v_2$) in Au+Au collisions at $\sqrt{s}=200$AGeV, with the UrQMD model. In this approach, the true event plane is known and both the non-flow effects and event-by-event spatial ($\epsilon$) and $v_2$ fluctuations exist. Qualitatively, the hierarchy of $v_2$'s from two, four and six-particle cumulants is consistent with the STAR data, however, the magnitude of $v_2$ in the UrQMD model is only 60% of the data. We find that the four and six-particle cumulants are good measures of the real elliptic flow over a wide range of centralities except for the most central and very peripheral events. There the cumulant method is affected by the $v_2$ fluctuations. In mid-central collisions, the four and six-particle cumulants are shown to give a good estimation of the true differential $v_2$, especially at large transverse momentum, where the two-particle cumulant method is heavily affected by the non-flow effects.Comment: 7 pages, 7 figures, revtex 4; The discussion on the non-flow effects is extended, a new figure (Fig.3) on v2-eccentricity correlation is added, accepted for publication in Phys. Rev.

State space formulas for stable rational matrix solutions of a Leech problem

Given stable rational matrix functions $G$ and $K$, a procedure is presented to compute a stable rational matrix solution $X$ to the Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and $\sup_{|z|\leq 1}\|X(z)\|\leq 1$. The solution is given in the form of a state space realization, where the matrices involved in this realization are computed from state space realizations of the data functions $G$ and $K$.Comment: 25 page