On the Second Fundamental Theorem of Asset Pricing

Let $X^1,\ldots, X^d$ be sigma-martingales on $(\Omega,{\cal F}, P)$. We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation w.r.t. $X^1,\ldots, X^d$ if and only if there is no equivalent probability measure (other than $P$) under which $X^1,\ldots,X^d$ are sigma-martingales. From this we deduce the second fundamental theorem of asset pricing- that completeness of a market is equivalent to uniqueness of Equivalent Sigma-Martingale Measure (ESMM)

Controller Design Using Adaptive Random Search for Close-Coupled Formation Flight

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76190/1/AIAA-11377-210.pd

Genome-wide Analyses Identify KIF5A as a Novel ALS Gene

To identify novel genes associated with ALS, we undertook two lines of investigation. We carried out a genome-wide association study comparing 20,806 ALS cases and 59,804 controls. Independently, we performed a rare variant burden analysis comparing 1,138 index familial ALS cases and 19,494 controls. Through both approaches, we identified kinesin family member 5A (KIF5A) as a novel gene associated with ALS. Interestingly, mutations predominantly in the N-terminal motor domain of KIF5A are causative for two neurodegenerative diseases: hereditary spastic paraplegia (SPG10) and Charcot-Marie-Tooth type 2 (CMT2). In contrast, ALS-associated mutations are primarily located at the C-terminal cargo-binding tail domain and patients harboring loss-of-function mutations displayed an extended survival relative to typical ALS cases. Taken together, these results broaden the phenotype spectrum resulting from mutations in KIF5A and strengthen the role of cytoskeletal defects in the pathogenesis of ALS.Peer reviewe

Case Report - Inflammatory pseudotumor of the mesentry

Inflammatory pseudotumor is a benign, chronic, inflammatory disorder known by many names. This condition presents with features suggestive of malignant disease. But surgery is curative for this condition. We report a case of inflammatory pseudotumour of the mesentry and retroperitoneum in a 40 year-old patient for whom curative resection was done

Introduction to stochastic calculus

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic

Synthesis and Antimicrobial Activity ofSome New 2-Substituted Benzothiazole Derivatives

Some new 2-(5-substituted-1,3,4-oxadiazole-2-yl)-1,3- benzothiazole (3a-j) were synthesized by refluxing benzothiazolyl carboxyhydrazide with different aryl acids in phosphoryl chloride. Structures of the synthesized compounds were established on the basis of 1H NMR and Mass spectral data. The anti microbial activity of the synthesized compounds was evaluated by disc diffusion method