We study a problem related to asset-liability management in life insurance. As shown by Wüthrich, Bühlmann and Furrer in [1], an insurance company can guarantee solvency by purchasing a Margrabe option enabling it to exchange its asset portfolio for a valuation portfolio. The latter can be viewed as a replicating portfolio for the insurance liabilities in terms of financial instruments. Our objective in this paper is to investigate numerically a valuation technique for such an option in a situation when the insurance company is a “large” investor, implying that its trading decisions can affect asset prices. We view this situation through the framework employed in the Cvitanic and Ma’s 1996 paper [2] and use the method of finite differences to solve the resulting non-linear PDE. Our results show reliability of this numerical method. Also we find, similarly to other authors, that the option price for the large investor is higher than that for a Black-Scholes trader. This makes it particularly compelling for a large insurance company to purchase a Margrabe option at the Black-Scholes price.

Abstract:
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an explicit formula for the root-mean-square amplitude of the expected fluctuations in the autocorrelation function. These fluctuations turn out to be $O(\hbar^{1/2})$ in the small $\hbar$ (high energy) limit. For comparison, any corrections due to scars from isolated periodic orbits would also be $O(\hbar^{1/2})$. The fluctuations take on a particularly simple form if the autocorrelation function is averaged over the direction of the separation vector. We compare our various predictions with recent numerical computations of Li and Robnik for the Robnik billiard, and find good agreement. We indicate how our results generalize to higher dimensions.

Abstract:
Consider a financial market in which an agent trades with utility-induced restrictions on wealth. For a utility function which satisfies the condition of reasonable asymptotic elasticity at $-\infty$ we prove that the utility-based super-replication price of an unbounded (but sufficiently integrable) contingent claim is equal to the supremum of its discounted expectations under pricing measures with finite {\it loss-entropy}. For an agent whose utility function is unbounded from above, the set of pricing measures with finite loss-entropy can be slightly larger than the set of pricing measures with finite entropy. Indeed, the former set is the closure of the latter under a suitable weak topology. Central to our proof is the representation of a cone $C_U$ of utility-based super-replicable contingent claims as the polar cone to the set of finite loss-entropy pricing measures. The cone $C_U$ is defined as the closure, under a relevant weak topology, of the cone of all (sufficiently integrable) contingent claims that can be dominated by a zero-financed terminal wealth. We investigate also the natural dual of this result and show that the polar cone to $C_U$ is generated by those separating measures with finite loss-entropy. The full two-sided polarity we achieve between measures and contingent claims yields an economic justification for the use of the cone $C_U$, and an open question.

Abstract:
This paper develops a probabilistic anticipation algorithm for dynamic objects observed by an autonomous robot in an urban environment. Predictive Gaussian mixture models are used due to their ability to probabilistically capture continuous and discrete obstacle decisions and behaviors; the predictive system uses the probabilistic output (state estimate and covariance) of a tracking system, and map of the environment to compute the probability distribution over future obstacle states for a specified anticipation horizon. A Gaussian splitting method is proposed based on the sigma-point transform and the nonlinear dynamics function, which enables increased accuracy as the number of mixands grows. An approach to caching elements of this optimal splitting method is proposed, in order to enable real-time implementation. Simulation results and evaluations on data from the research community demonstrate that the proposed algorithm can accurately anticipate the probability distributions over future states of nonlinear systems.

Abstract:
A novel u-shaped single element antenna having two feed ports is compared with two equal length monopoles separated by a distance equivalent to the width. A discussion of relative performance metrics is provided for MIMO applications, and measured data is given for comparison. Good impedance match and isolation of greater than ？10 dB are observed over the operating bandwidth from 2.3 to 2.39 GHz. The antenna patterns are highly uncorrelated, as illustrated by computation of the antenna pattern correlation coefficient for the two comparison monopoles.

Abstract:
Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on correlation length, we extract finite, calculable contributions to the entanglement entropy for a scalar field between the interior and exterior of a spatial domain of arbitrary shape. The leading term is proportional to the area of the dividing boundary; we also extract finite subleading contributions for a field defined in the bulk interior of a waveguide in 3+1 dimensions, including terms proportional to the waveguide's cross-sectional geometry; its area, perimeter length, and integrated curvature. We also consider related quantities at criticality and suggest a class of systems for which these contributions might be measurable.

Abstract:
We examine the hypothesis that inflation is primarily driven by vacuum energy at a scale indicated by gauge coupling unification. Concretely, we consider a class of hybrid inflation models wherein the vacuum energy associated with a grand unified theory condensate provides the dominant energy during inflation, while a second "inflaton" scalar slow-rolls. We show that it is possible to obtain significant tensor-to-scalar ratios while fitting the observed spectral index.

Abstract:
Consider a financial market in which an agent trades with utility-induced restrictions on wealth. By introducing a general convex-analytic framework which includes the class of umbrella wedges in certain Riesz spaces and faces of convex sets (consisting of probability measures), together with a duality theory for polar wedges, we provide a representation of the super-replication price of an unbounded (but sufficiently integrable) contingent claim that can be dominated approximately by a zero-financed terminal wealth as the the supremum of its discounted expectation under pricing measures which appear as faces of a given set of separating probability measures. Central to our investigation is the representation of a wedge $C_\Phi$ of utility-based super-replicable contingent claims as the polar wedge of the set of finite entropy separating measures. Our general approach shows, that those terminal wealths need {\it not} necessarily stem from {\it admissible} trading strategies only. The full two-sided polarity we achieve between measures and contingent claims yields an economic justification for the use of the wedge $C_\Phi$: the utility-based restrictions which this wedge imposes on terminal wealth arise only from the investor's preferences to asymptotically large negative wealth.

Abstract:
Rheumatoid arthritis (RA) is a condition characterized by chronic inflammation and proliferation of synovial membranes. The disease has a worldwide distribution, although it appears to show higher prevalence rates in specific populations (for example, indigenous Americans [1]). A strong genetic component is suspected, based on twin studies, studies of specific gene loci (such as the human leukocyte antigen (HLA) locus), and, more recently, gene linkage and genome-wide association studies [2,3]. Patients are heterogeneous in their clinical presentation, clinical course, response to therapy, and co-morbidities such as premature atherosclerosis [4] and an increased risk for specific cancers [5,6]. Together, these features make RA a paradigmatic 'complex trait' and amenable to investigation using systems biology approaches (that is, approaches designed to acquire a global view of the disease process rather than focus on specific cell interactions or metabolic pathways). Indeed, given its complexity, it seems unlikely that unraveling the most compelling and vexing questions about RA will occur using the 'single receptor-single pathway' approach that has been successful in other branches of biology and medicine.The 'completion' of the Human Genome Project held great promise, but, unfortunately, elucidating the sequence of the human genome has not led to as complete an understanding of cell biology and human disease as some thought it would. However, the undertaking of major efforts to elucidate genome function, particularly functional aspects of non-coding regions of the genome (for example, the National Institutes of Health Encyclopedia of DNA Elements (ENCODE) project), carries with it the potential to provide pathogenic insights that the understanding of the sequence and sequence variants has not. The application of these new results carries the potential to revolutionize our understanding of complex human conditions such as RA. Thus, any survey of where we have gone a

Abstract:
We survey observational constraints on the parameter space of inflation and axions and map out two allowed windows: the classic window and the inflationary anthropic window. The cosmology of the latter is particularly interesting; inflationary axion cosmology predicts the existence of isocurvature fluctuations in the CMB, with an amplitude that grows with both the energy scale of inflation and the fraction of dark matter in axions. Statistical arguments favor a substantial value for the latter, and so current bounds on isocurvature fluctuations imply tight constraints on inflation. For example, an axion Peccei-Quinn scale of 10^16 GeV excludes any inflation model with energy scale > 3.8*10^14 GeV (r > 2*10^(-9)) at 95% confidence, and so implies negligible gravitational waves from inflation, but suggests appreciable isocurvature fluctuations.