on the l p solvability of higher order parabolic and elliptic systems with bmo coefficients we prove the solvability in sobolev spaces for both divergence and non divergence form higher order parabolic and elliptic systems in the whole space on a half space and on a bounded domain the leading coefficients are assumed to be merely measurable only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders for the proof we develop a set of new techniques to produce mean oscillation estimates for systems on a half space

on the spanning property of risk bonds priced by equilibrium we propose a method of pricing financial securities written on nontradable underlyings such as temperature or precipitation levels to this end we analyze a financial market where agents are exposed to financial and nonfinancial risk factors the agents hedge their financial risk in the stock market and trade a risk bond issued by an insurance company from the issuer s point of view the bond s primary purpose is to shift insurance risks related to noncatastrophic weather events to financial markets as such its terminal payoff and yield curve depend on an underlying climate or temperature process whose dynamics are independent of the randomness driving stock prices we prove that if the bond s payoff function is monotone in the external risk process it can be priced by an equilibrium approach the equilibrium market price of climate risk and the equilibrium price process are characterized as solutions of nonlinear backward stochastic differential equations bsdes transferring the bsdes into partial differential equations pdes we represent the bond prices as smooth functions of the underlying risk factors our analytical results make the model amenable to a numerical analysis

elliptic equations with measurable coefficients in reifenberg domains abstract we prove w 1 p estimates for elliptic equations in divergence form under the assumption that for each point and for each sufficiently small scale there is a coordinate system so that the coefficients have small oscillation in n 1 directions we assume the boundary to be reifenberg flat and the coefficients having small oscillation in the flat direction of the boundary

parameter determination for complex number theoretic transforms using cyclotomic polynomials some new results for finding all convenient moduli m for a complex numbertheoretic transform with given transform length n and given primitive nth root of unity modulo m are presented the main result is based on the prime factorization for values of cyclotomic polynomials in the ring of gaussian integers

higher integrability result for nonlinear elliptic systems with conormal boundary conditions abstract we prove a boundary higher integrability result for nonlinear elliptic systems with conormal boundary conditions in locally uniform domains to do it we derive a boundary version of gehring giaquinta modica lemma and sobolev poincare type inequality in locally uniform domains our result plays a key role for handling the coefficients when obtaining caldero n zygmund type estimates with conormal boundary conditions in nonsmooth domains

deconvolution by successive approximations although various methods of deconvolution have been known for many years they are not generally regarded as being routinely usable the successive approximation method described in this article should be an improvement in that respect it operates in the time domain and is based on a simple procedure i first discuss the mathematics involved and then give some examples to illustrate how the method works and some of the things it can do

existence results for some quasilinear parabolic equations on considere le probleme de cauchy pour une equation dont la partie principale est un operateur parabolique quasilineaire le terme non lineaire additionnel a au plus une croissance quadratique par rapport au gradient de la solution on demontre l existence d une solution bornee faible sous des hypotheses de regularite minimales en supposant l existence d une sous solution et d une supersolution pour le probleme

area time efficient architecture of fft based montgomery multiplication the modular multiplication operation is the most time consuming operation for number theoretic cryptographic algorithms involving large integers such as rsa and diffie hellman implementations reveal that more than 75 percent of the time is spent in the modular multiplication function within the rsa for more than 1 024 bit moduli there are fast multiplier architectures to minimize the delay and increase the throughput using parallelism and pipelining however such designs are large in terms of area and low in efficiency in this paper we integrate the fast fourier transform fft method into the mclaughlin s framework and present an improved fft based montgomery modular multiplication mmm algorithm achieving high area time efficiency compared to the previous fft based designs we inhibit the zero padding operation by computing the modular multiplication steps directly using cyclic and nega cyclic convolutions thus we reduce the convolution length by half furthermore supported by the number theoretic weighted transform the fft algorithm is used to provide fast convolution computation we also introduce a general method for efficient parameter selection for the proposed algorithm architectures with single and double butterfly structures are designed obtaining low area latency solutions which we implemented on xilinx virtex 6 fpgas the results show that our work offers a better area latency efficiency compared to the state of the art fft based mmm architectures from and above 1 024 bit operand sizes we have obtained area latency efficiency improvements up to 50 9 percent for 1 024 bit 41 9 percent for 2 048 bit 37 8 percent for 4 096 bit and 103 2 percent for 7 680 bit operands furthermore the operating latency is also outperformed with high clock frequency for length 64 transform and above

dynamic programming and pricing of contingent claims in an incomplete market the problem of pricing contingent claims or options from the price dynamics of certain securities is well understood in the context of a complete financial market this paper studies the same problem in an incomplete market when the market is incomplete prices cannot be derived from the absence of arbitrage since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolio of the basic securities in this situation there is a price range for the actual market price of the contingent claim the maximum and minimum prices are studied using stochastic control methods the main result of this work is the determination that the maximum price is the smallest price that allows the seller to hedge completely by a controlled portfolio of the basic securities a similar result is obtained for the minimum price which corresponds to the purchase price

robust portfolio choice and indifference valuation we solve theoretically and numerically the problems of optimal portfolio choice and indifference valuation in a general continuous time setting the setting features i ambiguity and time consistent ambiguity averse preferences ii discontinuities in the asset price processes with a general and possibly infinite activity jump part next to a continuous diffusion part and iii general and possibly nonconvex trading constraints we characterize our solutions as solutions to backward stochastic differential equations bsdes generalizing kobylanski s result for quadratic bsdes to an infinite activity jump setting we prove existence and uniqueness of the solution to a general class of bsdes encompassing the solutions to our portfolio choice and valuation problems as special cases we provide an explicit decomposition of the excess return on an asset into a risk premium and an ambiguity premium and a further decomposition into a piece stemming from the diffusion part and a piece stemming from the ju

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

an equilibrium model for spot and forward prices of commodities we consider a market model that consists of financial investors and producers of a commodity producers optionally store some production for future sale and go short on forward contracts to hedge the uncertainty of the future commodity price financial investors take positions in these contracts to diversify their portfolios the spot and forward equilibrium commodity prices are endogenously derived as the outcome of the interaction between producers and investors assuming that both are utility maximizers we first prove the existence of an equilibrium in an abstract setting then in a framework where the consumers demand and the exogenously priced financial market are correlated we provide semi explicit expressions for the equilibrium prices and analyze their dependence on the model parameters the model can explain why increased investors participation in forward commodity markets and higher correlation between the commodity and the stock market could result in higher spot prices and lower forward premia

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

equilibrium pricing in incomplete markets under translation invariant preferences we propose a general discrete time framework for deriving equilibrium prices of financial securities it allows for heterogeneous agents unspanned random endowments and convex trading constraints we give a dual characterization of equilibria and provide general results on their existence and uniqueness in the special case where all agents have preferences of the same type and in equilibrium all random endowments are replicable by trading in the financial market we show that a one fund theorem holds and give an explicit expression for the equilibrium pricing kernel

localising temperature risk abstracton the temperature derivative market modeling temperature volatility is an important issue for pricing and hedging to apply the pricing tools of financial mathematics one needs to isolate a gaussian risk factor a conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern the object of this research is to estimate this heteroscedastic function so that after scale normalization a pure standardized gaussian variable appears earlier works investigated temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the variance process well therefore we consider a local adaptive modeling approach to find at each time point an optimal smoothing parameter to

an iterative error free algorithm to solve vandermonde systems the paper describes an algorithm to solve vandermonde system of linear equations the algorithm is error free i e it does not introduce either rounding off errors or errors caused by finite length of computer word into the solution cost analysis and its comparison to alternative error free method are included

global gradient estimates for general nonlinear parabolic equations in nonsmooth domains we establish the natural calderon zygmund theory for a nonlinear parabolic equation of p laplacian type in divergence form 0 1 ut diva du x t div f p 2f in t by essentially proving that 0 2 f p lq t du p lq t for every q 1 the equation under consideration is of general type and not necessarily of variation form the involved nonlinearity a a x t is assumed to have a small bmo semi norm with respect to x t variables and the lateral boundary of the domain is assumed to be reifenberg flat as a consequence we are able to not only relax the known regularity requirements on the nonlinearity for such a regularity theory but also extend local results to a global one in a nonsmooth domain whose boundary has a fractal property we also find an optimal regularity estimate in orlicz sobolev spaces for such nonlinear parabolic problems

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

precise deconvolution using the fermat number transform abstract a new algorithm to solve convolution systems of linear equations is described modular arithmetic and the fermat number theoretical transform are used the algorithm permits elimination of the rounding off errors of the solution of the deconvolution problem

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

elliptic equations with measurable nonlinearities in nonsmooth domains abstract we study elliptic equations with measurable nonlinearities in nonsmooth domains we establish an optimal global w 1 p estimate under the condition that the associated nonlinearity is allowed to be merely measurable in one variable but has a sufficiently small bmo semi norm in the other variables while the underlying domain is sufficiently flat in the reifenberg sense that the boundary of the domain is locally trapped between two narrow strips

elliptic equations in divergence form with partially bmo coefficients the solvability in sobolev spaces is proved for divergence form second order elliptic equations in the whole space a half space and a bounded lipschitz domain for equations in the whole space or a half space the leading coefficients aij are assumed to be only measurable in one direction and have locally small bmo semi norms in the other directions for equations in a bounded domain additionally we assume that aij have small bmo semi norms in a neighborhood of the boundary of the domain we give a unified approach of both the dirichlet boundary problem and the conormal derivative problem we also investigate elliptic equations in sobolev spaces with mixed norms under the same assumptions on the coefficients

number theoretic transforms of prescribed length on presente une methode constructive de recherche des modules appropries des transformations de la theorie des nombres de longueur donnee on utilise la factorisation primitive des polynomes cyclotomiques

parameter space for the architecture of fft based montgomery modular multiplication modular multiplication is the core operation in public key cryptographic algorithms such as rsa and the diffie hellman algorithm the efficiency of the modular multiplier plays a crucial role in the performance of these cryptographic methods in this paper improvements to fft based montgomery modular multiplication fftm 3 using carry save arithmetic and pre computation techniques are presented moreover pseudo fermat number transform is used to enrich the supported operand sizes for the fftm 3 the asymptotic complexity of our method is o l log l log log l which is the same as the schonhage strassen multiplication algorithm ssa a systematic procedure to select suitable parameter set for the fftm 3 is provided prototypes of the improved fftm 3 multiplier with appropriate parameter sets are implemented on xilinx virtex 6 fpga our method can perform 3 100 bit and 4 124 bit modular multiplications in 6 74 and 7 78 mu s respectively it offers better computation latency and area latency product compared to the state of the art methods for operand size of 3 072 bit and above

boundary riesz potential estimates for elliptic equations with measurable nonlinearities abstract we consider elliptic equations with measurable nonlinearities in a half cube q 2 r x 1 x r n x 1 0 where the boundary data is given on q 2 r x 1 x r n x 1 0 we obtain a point wise estimate of the gradient in terms of riesz potential of the right hand side data and the oscillation of the gradient of the boundary data under the assumption that the nonlinearity is only allowed to be measurable in x 1 variable

k dimensional error free deconvolution using the fermat number transform abstract the paper presents the generalization of the one dimensional deconvolution algorithm using the fermat number transform for the k dimensional deconvolution the problems of how to express a k dimensional convolution system in the form of special matrix equation how to calculate the precise value of the matrix determinant and how to remove rounding off errors in the process of deconvolution are solved in the paper the results are used in the algorithm derivation

error free algorithms to solve special and general discrete systems of linear equations this paper presents a survey of error free algorithms to solve various systems of linear equations the presented algorithms do not introduce computational errors into the solution and thus they are well suited to solve ill conditioned linear systems the error free algorithms are based on modulo arithmetic two basic approaches have been investigated in the paper the first one is based on iterative scheme using one modulus only the other one is parallel and uses several moduli and the chinese theorem it is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals

global gradient estimates for parabolic equations with measurable nonlinearities abstract we establish a global calderon zygmund theory of nonlinear parabolic equations with measurable nonlinearities in divergence form by proving that the spatial gradient of a weak solution is as integrable as the inhomogeneous term nonlinearity a x t is assumed to be only measurable in one spatial variable and has locally small bmo semi norm in the other spatial and time variables uniformly with respect to variable the boundary of the bounded domain can be beyond the lipschitz category but it is well trapped in two narrow strips at each point and at each scale

bsde with quadratic growth and unbounded terminal value in this paper we study the existence of solution to bsde with quadratic growth and unbounded terminal value the main idea consists in using a localization procedure together with a priori bounds

continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations using the maximum principle for semicontinuous functions 3 4 we prove a general continuous dependence on the nonlinearities estimate for bounded holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations furthermore we provide existence uniqueness and holder continuity results for bounded viscosity solutions of such equations our results are general enough to encompass hamilton jacobi bellman isaacs s equations of zero sum two player stochastic dierential games an immediate conse quence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations

non lipschitz minimizers of smooth uniformly convex functionals we construct non lipschitz minimizers of smooth uniformly convex functionals of type i u f du x dx our method is based on the use of null lagrangians

backward stochastic differential equations and partial differential equations with quadratic growth we provide existence comparison and stability results for one dimensional backward stochastic differential equations bsdes when the coefficient or generator f t y z is continuous and has a quadratic growth in z and the terminal condition is bounded we also give in this framework the links between the solutions of bsdes set on a diffusion and viscosity or sobolev solutions of the corresponding semilinear partial differential equations

exact deconvolution using number theoretic transforms abstract using residue arithmetic and number theoretic transforms new algorithms of the one and two dimensional deconvolution are described these algorithms work without round off errors and yield the exact solution under natural conditions by the same method the exact value of the determinant of a circulant integer matrix is computed too

calderon zygmund estimates for parabolic measure data equations abstract we consider parabolic equations of the type u t div a x t d u having a radon measure on the right hand side and prove fractional integrability and differentiability results of calderon zygmund type for weak solutions we extend some of the integrability results for elliptic equations achieved by g mingione 2007 24 to the parabolic setting and locally recover the integrability results of l boccardo a dall aglio t gallouet and l orsina 1997 in 5

higher order elliptic and parabolic systems with variably partially bmo coefficients in regular and irregular domains abstract the solvability in sobolev spaces is proved for divergence form complex valued higher order parabolic systems in the whole space on a half space and on a reifenberg flat domain the leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder the directions in which the coefficients are only measurable vary depending on each cylinder the corresponding elliptic problem is also considered

second order backward stochastic differential equations and fully nonlinear parabolic pdes for a d dimensional diffusion of the form dxt xt dt xt dwt and continuous functions f and g we study the existence and uniqueness of adapted processes y z and a solving the second order backward stochastic differential equation 2bsde dyt f t xt yt zt t dt z dxt t 0 t dzt at dt t dxt

global gradient estimates for nonlinear equations of p laplace type from composite materials abstract we study global gradient estimates for the weak solution to divergence form nonlinear elliptic equations with p growth nonlinearities from composite materials we assume that the domain is bounded and is composed of disjoint reifenberg flat domains and the nonlinearities have small bmo seminorms in each subdomain under these assumptions based on our new geometric observation for disjoint reifenberg domains and gradient estimates for nonlinear equations with measurable p growth nonlinearities we establish global w 1 q estimates for p q