520 research outputs found
Dual representations for general multiple stopping problems
In this paper, we study the dual representation for generalized multiple
stopping problems, hence the pricing problem of general multiple exercise
options. We derive a dual representation which allows for cashflows which are
subject to volume constraints modeled by integer valued adapted processes and
refraction periods modeled by stopping times. As such, this extends the works
by Schoenmakers (2010), Bender (2011a), Bender (2011b), Aleksandrov and Hambly
(2010), and Meinshausen and Hambly (2004) on multiple exercise options, which
either take into consideration a refraction period or volume constraints, but
not both simultaneously. We also allow more flexible cashflow structures than
the additive structure in the above references. For example some exponential
utility problems are covered by our setting. We supplement the theoretical
results with an explicit Monte Carlo algorithm for constructing confidence
intervals for the price of multiple exercise options and exemplify it by a
numerical study on the pricing of a swing option in an electricity market.Comment: This is an updated version of WIAS preprint 1665, 23 November 201
Measure and integral : new foundations after one hundred years
The present article aims to describe the main ideas and developments in the theory of measure and integral in the course and at the end of the first century of its existence
Frobenius actions on the de Rham cohomology of Drinfeld modules
We study the action of endomorphisms of a Drinfeld A-module \phi on its de Rham cohomology H_{DR}(\phi,L) and related modules, in the case where \phi is defined over a field L of finite A-characteristic \mathfrak{p}. Among others, we find that the nilspace H_{0} of the total Frobenius Fr_{DR} on H_{DR}(\phi,L) \mathfrak{p} has dimension h = height of \phi. We define and study a pairing between the \mathfrak{p}-torsion _{\mathfrak{p}}\phi of \phi and H_{DR}(\phi,L), which becomes perfect after dividing out H_{0}
Wigner chaos and the fourth moment
We prove that a normalized sequence of multiple Wigner integrals (in a fixed
order of free Wigner chaos) converges in law to the standard semicircular
distribution if and only if the corresponding sequence of fourth moments
converges to 2, the fourth moment of the semicircular law. This extends to the
free probabilistic, setting some recent results by Nualart and Peccati on
characterizations of central limit theorems in a fixed order of Gaussian Wiener
chaos. Our proof is combinatorial, analyzing the relevant noncrossing
partitions that control the moments of the integrals. We can also use these
techniques to distinguish the first order of chaos from all others in terms of
distributions; we then use tools from the free Malliavin calculus to give
quantitative bounds on a distance between different orders of chaos. When
applied to highly symmetric kernels, our results yield a new transfer
principle, connecting central limit theorems in free Wigner chaos to those in
Gaussian Wiener chaos. We use this to prove a new free version of an important
classical theorem, the Breuer-Major theorem.Comment: Published in at http://dx.doi.org/10.1214/11-AOP657 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A formula for the probability of the exponents of finite p-groups
In this paper, I will introduce a link between the volume of a finite p-group in the Cohen-Lenstra measure and partitions of a certain type. These partitions will be classified by the output of an algorithm. As a corollary, I will give a formula for the probability of a p-group to have a specific exponent
On the torsion of optimal elliptic curves over function fields
For an optimal elliptic curve E over \mathbb{F}_{q}(t) of conductor \mathfrak{p}\cdot\infty, where \mathfrak{p} is prime, we show that E(F)_{tor} is generated by the image of the cuspidal divisor group
Estimates of the second-order derivatives for solutions to the two-phase parabolic problem
The L_{\infty}-estimates of the second derivatives for solutions of the parabolic free boundary problem with two phases
\Delta u-\partial_{t}u=\lambda^{+}\chi_{\left\{ u>0\right\} }-\lambda^{-}\chi_{\left\{ u<0\right\} }\textrm{in }B_{1}^{+}\times]-1,0],\textrm{ }\lambda^{\pm}\geq0,\lambda^{+}+\lambda^{-}>0,
satisfying the non-zero Dirichlet condition on \Pi_{1}:=\left\{ (x,t):\left|x\right|\leq1,x_{1}=0,-1<t\leq0\right\}, are proved
Partial regularity for local minimizers of splitting-type variational integrals
We consider local minimizers u:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{N} of anisotropic variational integrals of (p,q)-growth with exponents 2\leq p\leq q\leq\mbox{min}\left\{ 2+p,p\frac{n}{n-2}\right\}. If the integrand is of splitting-type, then partial C^{1}-regularity of u is established
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