Hull Consistency Under Monotonicity

International audienceWe prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example

Pricing Discretely Monitored Asian Options by Maturity Randomization

We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Levy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Levy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a recursive theoretical formula for the moments to check the accuracy of the results. We compare the implementation of our method to Monte Carlo simulation implemented with control variates and using different parametric Levy processes. We also discuss model-risk issues

q-Breathers in Discrete Nonlinear Schroedinger arrays with weak disorder

Nonlinearity and disorder are key players in vibrational lattice dynamics, responsible for localization and delocalization phenomena. $q$-Breathers -- periodic orbits in nonlinear lattices, exponentially localized in the reciprocal linear mode space -- is a fundamental class of nonlinear oscillatory modes, currently found in disorder-free systems. In this paper we generalize the concept of $q$-breathers to the case of weak disorder, taking the Discrete Nonlinear Schr\"{o}dinger chain as an example. We show that $q$-breathers retain exponential localization near the central mode, provided that disorder is sufficiently small. We analyze statistical properties of the instability threshold and uncover its sensitive dependence on a particular realization. Remarkably, the threshold can be intentionally increased or decreased by specifically arranged inhomogeneities. This effect allows us to formulate an approach to controlling the energy flow between the modes. The relevance to other model arrays and experiments with miniature mechanical lattices, light and matter waves propagation in optical potentials is discussed.Comment: 5 pages, 3 figure

Prevention of mucositis in bone marrow transplantation: A double blind randomised controlled trial of sucralfate

Mucositis is still a leading side effect of high dose chemotherapy and irradiation delivered in autologous and allogeneic bone marrow transplantation. In this double blind randomised study, we tested the efficacy of sucralfate for the prevention of mucositis induced by such conditioning treatments. Treatment was started one day before conditioning regimen and patients were prospectively evaluated. The main endpoint was severe mucositis that was more frequent in the placebo group than in the sucralfate group (47% vs. 29%, P = 0.07). This trend was confirmed after adjustment on total body irradiation (TBI) (P = 0.06), the sole stratification parameter. Interestingly, patients receiving sucralfate showed a significant reduction of diarrhoea (25% vs. 53%, P = 0.005). Overall, the preventive administration of sucralfate appears to be an effective proce dure to diminish the occurrence of severe oral and intestinal mucositis in patients treated by high dose chemotherapy alone or combined with TBI before bone marrow transplantatio

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

Casimir force in critical ternary polymer solutions

Consider a mixture of two incompatible polymers A and B in a common good solvent, confined between two parallel plates separated by a finite distance L. We assume that these plates strongly attract one of the two polymers close to the consolute point (critical adsorption). The plates then experience an effective force resulting from strong fluctuations of the composition. To simplify, we suppose that either plates have the same preference to attract one component (symmetric plates) or they have an opposed preference (asymmetric plates). The force is attractive for symmetric plates and repulsive for asymmetric ones. We first exactly compute the force using the blob model, and find that the attractive and repulsive forces decay similarly to L⁻⁴. To go beyond the blob model that is a mean-field theory, and in order to get a correct induced force, we apply the Renormalization-Group to a φ⁴ -field theory ( φ is the composition fluctuation), with two suitable boundary conditions at the surfaces. The main result is that the expected force is the sum of two contributions. The first one is the mean-field contribution decaying as L⁻⁴, and the second one is the force deviation originating from strong fluctuations of the composition that decreases rather as L⁻³. This implies the existence of some cross-over distance L* ∼ aNφ¹/² ( a is the monomer size, N is the polymerization degree of chains and φ is the monomer volumic fraction), which separates two distance-regimes. For small distances (L L*) the fluctuation force is more important.Розглядається суміш двох несумісних полімерів A і B , що добре розчиняються в спільному розчиннику, вміщена між двома паралельними пластинами, розділеними скінченною відстанню L. Ми вважаємо, що поблизу точки розчинення вони сильно притягають один з двох полімерів (критична адсорбція). При цьому пластини знаходяться під впливом ефективної сили, породженої сильними флуктуаціями суміші. Для спрощення ми припускаємо, що або обидві пластини притягають той самий компонент (симетричні пластини) або вони віддають перевагу різним компонентам (асиметричні пластини). Симетричним пластинам відповідає сила притягання, асиметричним – відштовхування. Спершу ми точно розрахували цю силу, використовуючи краплинну модель, і встановили, що сили притягання і відштовхування загасають подібним чином як L⁻⁴. Щоб вийти поза межі краплинної моделі, яка відповідає наближенню середнього поля, і з метою отримати правильний вигляд індукованої сили, ми застосували ренорм-груповий підхід до теорії поля φ⁴ ( φ – флуктуація суміші) з двома відповідними граничними умовами на поверхнях. У результаті встановлено, що шукана сила є сумою двох вкладів. Перший з них – це вклад середнього поля, що загасає якL⁻⁴, а другий – відхилення, викликане сильними флуктуаціями суміші, що зменшується радше як L⁻³. Це означає, що існує певна відстань кроссоверу L* ∼ aNφ¹/² ( a – розмір мономера, N – ступінь полімеризації ланцюжків і φ – об’ємна частка мономера), що розділяє характерні відстані двох згаданих режимів. На малих відстанях (L L*) більш важливим стає флуктуаційний вклад