Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

There is no Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs

Conventional wisdom holds that since continuous-time, Black-Scholes hedging is infinitely expensive in a model with proportional transaction costs, there is no continuous-time strategy which hedges a European call option perfectly. Of course, if one is attempting to dominate the European call rather than replicate it, then one can use the trivial strategy of buying one share of the underlying stock and holding to maturity. In this paper we prove that this is, in fact, the least expensive method of dominating a European call in a Black-Scholes model with proportional transaction costs

On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients

Convergence of Ginzburg-Landau functionals in 3-d superconductivity

In this paper we consider the asymptotic behavior of the Ginzburg- Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced model for the vortex density, and we deduce a curvature equation for the vortex lines. In a companion paper, we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H_{c1}, and the critical angular velocity of rotating Bose-Einstein condensates.Comment: 45 page

Vortex density models for superconductivity and superfluidity

We study some functionals that describe the density of vortex lines in superconductors subject to an applied magnetic field, and in Bose-Einstein condensates subject to rotational forcing, in quite general domains in 3 dimensions. These functionals are derived from more basic models via Gamma-convergence, here and in a companion paper. In our main results, we use these functionals to obtain descriptions of the critical applied magnetic field (for superconductors) and forcing (for Bose-Einstein), above which ground states exhibit nontrivial vorticity, as well as a characterization of the vortex density in terms of a non local vector-valued generalization of the classical obstacle problem.Comment: 34 page

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

Analogy making and the structure of implied volatility skew

An analogy based option pricing model is put forward. If option prices are determined in accordance with the analogy model, and the Black Scholes model is used to back-out implied volatility, then the implied volatility skew arises, which flattens as time to expiry increases. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew

Histone Deacetylase Inhibitors Downregulate Checkpoint Kinase 1 Expression to Induce Cell Death in Non-Small Cell Lung Cancer Cells

Background: Histone deacetylase inhibitors (HDACis) are promising anticancer drugs; however, the molecular mechanisms leading to HDACi-induced cell death have not been well understood and no clear mechanism of resistance has been elucidated to explain limited efficacy of HDACis in clinical trials. Methods and Findings: Here, we show that protein levels of checkpoint kinase 1 (Chk1), which has a major role in G2 cell cycle checkpoint regulation, was markedly reduced at the protein and transcriptional levels in lung cancer cells treated with pan-and selective HDACis LBH589, scriptaid, valproic acid, apicidin, and MS-275. In HDACi treated cells Chk1 function was impaired as determined by decreased inhibitory phosphorylation of cdc25c and its downstream target cdc2 and increased expression of cdc25A and phosphorylated histone H3, a marker of mitotic entry. In time course experiments, Chk1 downregulation occurred after HDACi treatment, preceding apoptosis. Ectopic expression of Chk1 overcame HDACiinduced cell death, and pretreating cells with the cdc2 inhibitor purvalanol A blocked entry into mitosis and prevented cell death by HDACis. Finally, pharmacological inhibition of Chk1 showed strong synergistic effect with LBH589 in lung cancer cells. Conclusions: These results define a pathway through which Chk1 inhibition can mediate HDACi-induced mitotic entry and cell death and suggest that Chk1 could be an early pharmacodynamic marker to assess HDACi efficacy in clinical samples