1,677 research outputs found
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
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