Hedging Pure Endowments with Mortality Derivatives

In recent years, a market for mortality derivatives began developing as a way to handle systematic mortality risk, which is inherent in life insurance and annuity contracts. Systematic mortality risk is due to the uncertain development of future mortality intensities, or {\it hazard rates}. In this paper, we develop a theory for pricing pure endowments when hedging with a mortality forward is allowed. The hazard rate associated with the pure endowment and the reference hazard rate for the mortality forward are correlated and are modeled by diffusion processes. We price the pure endowment by assuming that the issuing company hedges its contract with the mortality forward and requires compensation for the unhedgeable part of the mortality risk in the form of a pre-specified instantaneous Sharpe ratio. The major result of this paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting price as an expectation under an equivalent martingale measure. Another important result is that hedging with the mortality forward may raise or lower the price of this pure endowment comparing to its price without hedging, as determined in Bayraktar et al. [2009]. The market price of the reference mortality risk and the correlation between the two portfolios jointly determine the cost of hedging. We demonstrate our results using numerical examples.Comment: 33 Pages, 1 figur

Superplastic forming and diffusion bonding of rapidly solidified, dispersion strengthened aluminum alloys for elevated temperature structural applications

Rapidly solidified alloys, based upon the Al-Fe-V-Si system and designed for elevated temperature applications, were evaluated for superplasticity and diffusion bonding behavior. Alloys with 8, 16, 27, and 36 volume percent silicide dispersoids were produced; dispersoid condition was varied by rolling at 300, 400, and 500 C (572, 752, and 932 F). Superplastic behavior was evaluated at strain rates from 1 x 10(exp -6)/s to 8.5/s at elevated temperatures. The results indicate that there was a significant increase in elongation at higher strain rates and at temperatures above 600 C (1112 F). However, the exposure of the alloys to temperatures greater than 600 C (1112 F) resulted in the coarsening of the strengthening dispersoid and the degradation of mechanical properties. Diffusion bonding was possible using low gas pressure at temperatures greater than 600 C (1112 F) which also resulted in degraded properties. The bonding of Al-Fe-V-Si alloys to 7475 aluminum alloy was performed at 516 C (960 F) without significant degradation in microstructure. Bond strengths equal to 90 percent that of the base metal shear strength were achieved. The mechanical properties and microstructural characteristics of the alloys were investigated

Skip-Sliding Window Codes

Constrained coding is used widely in digital communication and storage systems. In this paper, we study a generalized sliding window constraint called the skip-sliding window. A skip-sliding window (SSW) code is defined in terms of the length $L$ of a sliding window, skip length $J$, and cost constraint $E$ in each sliding window. Each valid codeword of length $L + kJ$ is determined by $k+1$ windows of length $L$ where window $i$ starts at $(iJ + 1)$th symbol for all non-negative integers $i$ such that $i \leq k$; and the cost constraint $E$ in each window must be satisfied. In this work, two methods are given to enumerate the size of SSW codes and further refinements are made to reduce the enumeration complexity. Using the proposed enumeration methods, the noiseless capacity of binary SSW codes is determined and observations such as greater capacity than other classes of codes are made. Moreover, some noisy capacity bounds are given. SSW coding constraints arise in various applications including simultaneous energy and information transfer.Comment: 28 pages, 11 figure

Missing Thermal Energy of the Intracluster Medium

The Sunyaev-Zel'dovich (SZ) effect is a direct probe of thermal energy content of the Universe, induced in the cosmic microwave background (CMB) sky through scattering of CMB photons off hot electrons in the intracluster medium (ICM). We report a 9-sigma detection of the SZ signal in the CMB maps of Wilkinson Microwave Anisotropy Probe (WMAP) 3yr data, through study of a sample of 193 massive galaxy clusters with observed X-ray temperatures greater than 3 keV. For the first time, we make a model-independent measurement of the pressure profile in the outskirts of the ICM, and show that it closely follows the profiles obtained by X-ray observations and numerical simulations. We find that our measurements of the SZ effect would account for only half of the thermal energy of the cluster, if all the cluster baryons were in the hot ICM phase. Our measurements indicate that a significant fraction (35 +/- 8 %) of baryonic mass is missing from the hot ICM, and thus must have cooled to form galaxies, intracluster stars, or an unknown cold phase of the ICM. There does not seem to be enough mass in the form of stars or cold gas in the cluster galaxies or intracluster space, signaling the need for a yet-unknown baryonic component (at 3-sigma level), or otherwise new astrophysical processes in the ICM.Comment: 9 pages, 4 figures, references added, a mismatch between X-ray and SZ properties of simulated clusters is corrected, marginally increasing the significance of missing baryon fraction, Accepted for publication in MNRA

Spin dynamics in the antiferromagnetic phase for electron-doped cuprate superconductors

Based on the $t$-$t'$-$t''$-$J$ model we have calculated the dynamical spin susceptibilities in the antiferromagnetic (AF) phase for electron-doped cuprates, by use of the slave-boson mean-field theory and random phase approximation. Various results for the susceptibilities versus energy and momentum have been shown at different dopings. At low energy, except the collective spin-wave mode around $(\pi,\pi)$ and 0, we have primarily observed that new resonance peaks will appear around $(0.3\pi,0.7\pi)$ and equivalent points with increasing doping, which are due to the particle-hole excitations between the two AF bands. The peaks are pronounced in the transverse susceptibility but not in the longitudinal one. These features are predicted for neutron scattering measurements.Comment: 5 pages, 3 figures, published version with minor change

Restoration of Quantum State in Dephasing Channel

In this paper, we propose an explicit scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an N-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an N-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum state beyond the standard RU scheme.Comment: 8 pages, 2 figures, Typos and inaccuracies are corrected. Presentation is also improve

WMAP constraints on the Intra-Cluster Medium

We devise a Monte-Carlo based, optimized filter match method to extract the thermal Sunyaev-Zel'dovich (SZ) signature of a catalog of 116 low-redshift X-ray clusters from the first year data release of the Wilkinson Microwave Anisotropy Probe (WMAP). We detect an over-all amplitude for the SZ signal at the ~ 8-sigma level, yielding a combined constraint of f_{gas}h = 0.08 +/- 0.01 (ran) +/- 0.01 (sys) on the gas mass fraction of the Intra-Cluster Medium. We also compile X-ray estimated gas fractions from the literature for our sample, and find that they are consistent with the SZ estimates at the 2-sigma level, while both show an increasing trend with X-ray temperature. Nevertheless, our SZ estimated gas fraction is 30-40% smaller than the concordance LCDM cosmic average. We also express our observations in terms of the SZ flux-temperature relation, and compare it with other observations, as well as numerical studies. Based on its spectral and spatial signature, we can also extract the microwave point source signal of the clusters at the 3-sigma level, which puts the average microwave luminosity (at ~ 41 GHz) of bright cluster members (M_K < -21) at (2.4 +/- 0.8) x 10^{27} h^{-2} erg/s/Hz. Furthermore, we can constrain the average dark matter halo concentration parameter to c_{vir}=3.4+0.6-0.9, for clusters with T_x > 5 kev. Our work serves as an example for how correlation of SZ surveys with cluster surveys in other frequencies can significantly increase our physical understanding of the intra-cluster medium.Comment: 34 pages, 6 ps figures, Extended discussion of theoretical uncertainties, radio sources, and future prospects, Accepted for Publication in Ap