283 research outputs found

    An overview of Viscosity Solutions of Path-Dependent PDEs

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    This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]

    Systematic determination of the mosaic structure of bacterial genomes: species backbone versus strain-specific loops

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    BACKGROUND: Public databases now contain multitude of complete bacterial genomes, including several genomes of the same species. The available data offers new opportunities to address questions about bacterial genome evolution, a task that requires reliable fine comparison data of closely related genomes. Recent analyses have shown, using pairwise whole genome alignments, that it is possible to segment bacterial genomes into a common conserved backbone and strain-specific sequences called loops. RESULTS: Here, we generalize this approach and propose a strategy that allows systematic and non-biased genome segmentation based on multiple genome alignments. Segmentation analyses, as applied to 13 different bacterial species, confirmed the feasibility of our approach to discern the 'mosaic' organization of bacterial genomes. Segmentation results are available through a Web interface permitting functional analysis, extraction and visualization of the backbone/loops structure of documented genomes. To illustrate the potential of this approach, we performed a precise analysis of the mosaic organization of three E. coli strains and functional characterization of the loops. CONCLUSION: The segmentation results including the backbone/loops structure of 13 bacterial species genomes are new and available for use by the scientific community at the URL:

    Dry Markets and Superreplication Bounds of American Derivatives

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    This paper studies the impact of dry markets for underlying assets on the pricing of American derivatives, using a discrete time framework. Dry markets are characterized by the possibility of non-existence of trading at certain dates. Such non-existence may be deterministic or probabilistic. Using superreplicating strategies, we derive expectation representations for the range of arbitrage-free values of the dervatives. In the probabilistic case, if we consider an enlarged filtration induced by the price process and the market existence process, ordinary stopping times are required. If not, randomized stopping times are required. Several comparisons of the ranges obtained with the two market restrictions are performed. Finally, we conclude that arbitrage arguments are not enough to define the optimal exercise policy.N/

    Fractional smoothness and applications in finance

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    This overview article concerns the notion of fractional smoothness of random variables of the form g(XT)g(X_T), where X=(Xt)t∈[0,T]X=(X_t)_{t\in [0,T]} is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.Comment: Chapter of AMAMEF book. 20 pages

    On the Existence of Shadow Prices

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    For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless "shadow market" that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample which shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid-ask-spreads.Comment: 14 pages, 1 figure, to appear in "Finance and Stochastics

    Rhodococcus equi venous catheter infection: a case report and review of the literature

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    <p>Abstract</p> <p>Introduction</p> <p><it>Rhodococcus equi </it>is an animal pathogen that was initially isolated from horses and is being increasingly reported as a cause of infection in humans with impaired cellular immunity. However, this pathogen is underestimated as a challenging antagonist and is frequently considered to be a mere contaminant despite the potential for life-threatening infections. Most case reports have occurred in immunocompromised patients who have received organ transplants (for example kidney, heart, bone marrow) or those with human immunodeficiency virus infection. Infections often manifest as pulmonary involvement or soft tissue abscesses. Bacteremia related to <it>R. equi </it>infections of tunneled central venous catheters has rarely been described.</p> <p>Case presentation</p> <p>We report the case of a 63-year-old non-transplant recipient, non-HIV infected Caucasian woman with endometrial carcinoma who developed recurrent bloodstream infections and septic shock due to <it>R. equi </it>and ultimately required the removal of her port catheter, a subcutaneous implantable central venous catheter. We also review the medical literature related to human infections with <it>R. equi</it>.</p> <p>Conclusion</p> <p><it>R. equi </it>should be considered a serious pathogen, not a contaminant, particularly in an immunocompromised patient who presents with a central venous catheter-related bloodstream infection. Counseling patients with central venous catheters who participate in activities involving exposure to domesticated animals is recommended.</p

    Market consistent valuations with financial imperfection

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    In this paper, we study market consistent valuations in imperfect markets. In the first part of the paper, we observe that in an imperfect market one needs to distinguish two type of market consistencies, namely types I and II. We show that while market consistency of type I holds without very strong conditions, market consistency of type II (which in the literature is known as the usual definition of market consistency) is only well defined in perfect markets. This is important since the existing literature on market consistency considers perfect markets where the two market consistencies are equivalent. In the second part of the paper, by introducing a best estimator we find strong connections between hedging and market consistency of either type. We show under very general conditions, the type I and the type II market consistent evaluators are best estimators, and establish a two-step representation for the market consistent risk evaluators. In the third part of the paper, we present several families of market consistent evaluators in imperfect markets
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