local polynomial variance function estimation the conditional variance function in a heteroscedastic nonparametric regression model is estimated by linear smoothing of squared residuals attention is focused on local polynomial smoothers both the mean and variance functions are assumed to be smooth but neither is assumed to be in a parametric family the biasing effect of preliminary estimation of the mean is studied and a degrees of freedom correction of bias is proposed the corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known a proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions the proposal is illustrated with data from the lidar method of measuring atmospheric pollutants and from turbulence model computations

adaptive θ methods for pricing american options we develop adaptive q methods for solving the black scholes pde for american options by adding a small continuous term the black scholes pde becomes an advection diffusion reaction equation on a fixed spatial domain standard implementation of q methods would require a newton type iterative procedure at each time step thereby increasing the computational complexity of the methods our linearly implicit approach avoids such complications we establish a general framework under which q methods satisfy a discrete version of the positivity constraint characteristic of american options and numerically demonstrate the sensitivity of the constraint the positivity results are established for the single asset and independent two asset models in addition we have incorporated and analyzed an adaptive time step control strategy to increase the computational efficiency numerical experiments are presented for one and two asset american options using adaptive exponential splitting for two asset problems the approach is compared with an iterative solution of the two asset problem in terms of computational efficiency

the obstacle problem for a class of hypoelliptic ultraparabolic equations we study the obstacle problem for a class of degenerate parabolic operators with continuous coefficients this problem arises in the blackscholes framework when considering path dependent american

optimal convergence rate of the explicit finite difference scheme for american option valuation an optimal convergence rate o dx for an explicit finite difference scheme for a variational inequality problem is obtained under the stability condition s email protected dx 2 1 using completely pde methods as a corollary a binomial tree scheme of an american put option where s email protected dx 2 1 is convergent unconditionally with the rate o dt 1 2

assessing the adequacy of variance function in heteroscedastic regression models heteroscedastic data arise in many applications in heteroscedastic regression analysis the variance is often modeled as a parametric function of the covariates or the regression mean we propose a kernel smoothing type nonparametric test for checking the adequacy of a given parametric variance structure the test does not need to specify a parametric distribution for the random errors it is shown that the test statistic has an asymptotical normal distribution under the null hypothesis and is powerful against a large class of alternatives we suggest a simple bootstrap algorithm to approximate the distribution of the test statistic in finite sample size numerical simulations demonstrate the satisfactory performance of the proposed test we also illustrate the application by the analysis of a radioimmunoassay data set

counting lattice points of rational polyhedra abstract the generating function f p p zn x for a rational polytope p carries all essential information of p in this paper we show that for any positive integer n the generating function f p n of np nx x p can be written as f p n a p n x n where a is the set of all vertices of p and each p n is a certain periodic function of n the ehrhart reciprocity law follows automatically from the above formula we also present a formula for the coefficients of ehrhart polynomials in terms of elementary symmetric functions

convergence of binomial tree methods for european american path dependent options the binomial tree method first proposed by cox ross and rubinstein journal of financial economics 7 1979 pp 229 263 is one of the most popular approaches to pricing options by introducing an additional path dependent variable such methods can be readily extended to the valuation of path dependent options in this paper using numerical analysis and the notion of viscosity solutions we present a unifying theoretical framework to show the uniform convergence of binomial tree methods for european american path dependent options including arithmetic average options geometric average options and lookback options

lattice points in simple polytopes in terms of fp h q x dx where the polytope p h is obtained from p by independent parallel motions of all facets this extends to simple lattice polytopes the eulermaclaurin summation formula of khovanskii and pukhlikov 8 valid for lattice polytopes such that the primitive vectors on edges through each vertex of p form a basis of the lattice as a corollary we recover results of pommersheim 9 and kantor khovanskii 6 on the coefficients of the ehrhart polynomial of p our proof is elementary in a subsequent article we will show how to adapt it to compute the equivariant todd class of any complete toric variety with quotient singularities the euler maclaurin summation formula for simple lattice polytopes has been obtained independently by ginzburg guillemin karshon 4 they used the dictionary between convex polytopes and projective toric varieties with an ample divisor class in combination with the riemann roch kawasaki formula 1 7 for complex manifolds with quotient singularities a counting formula for lattice points in lattice simplices has been announced by cappell and shaneson 2 as a consequence of their computation of the todd class of toric varieties with quotient singularities

variance functions and the minimum detectable concentration in assays abstract assay data are often fit by a nonlinear regression model incorporating heterogeneity of variance as ion radioimmunoassay for example typically the standard deviation of the response is taken to be proportional to a power theta of the mean there is considerable empirical evidence suggesting that for assays of a reseasonable size how one estimates the parameter theta does not greatly affect how well one estimates the the mean regression function an additional component of assay analysis is the estimation of auxillary constructs such as the minimum detectable concentration for which many definitions exist we focus on one such definition the minimum detectable concentration depends both on theta and the mean regression function we compare three standard method of estimating the parameter theta due to rodbard 1978 raab 1981a and carroll and ruppert 1982b when duplicate counts are taken at each concentration the first method is only 20 efficient asymptotically in comparison to the third and the resulting estimate of the minimum detectable concentration is asymptotically 3 3 times more variable for first than the third less dramatic results obtain for the second estimator compared to the third this estimator is still not efficient however simulation results and an example are supportive of the asymptotic theory keywords least squares method

values of zeta functions at negative integers dedekind sums and toric geometry in the present paper we study relations among special values of zeta functions of real quadratic fields properties of generalized dedekind sums and todd classes of toric varieties the main theme of the paper is the use of toric geometry to explain in a conceptual way properties of the values of zeta functions and dedekind sums as well as to provide explicit computations both toric varieties and zeta functions associate numerical invariants to cones in lattices with different motivations and applications though we will focus on the case of two dimensional cones in the present paper we introduce notation and definitions that are valid for cones of arbitrary dimension the reason for this added generality is clarity as well as preparation for the results of a subsequent publication

score tests for heteroscedasticity in wavelet regression summary we consider two score tests for heteroscedasticity in the errors of a signal plus noise model where the signal is estimated by wavelet thresholding methods the error variances are assumed to depend on observed covariates through a parametric relationship of known form the tests are based on the approaches of breusch pagan 1979 and koenker 1981 we establish the asymptotic validity of the tests and examine their performance in a simulation study the koenker test is found to perform well in terms of both size and power

residue formulae vector partition functions and lattice points in rational polytopes we obtain residue formulae for certain functions of several vari ables as an application we obtain closed formulae for vector partition func tions and for their continuous analogs they imply an euler maclaurin sum mation formula for vector partition functions and for rational convex poly topes as well we express the sum of values of a polynomial function at all lattice points of a rational convex polytope in terms of the variation of the integral of the function over the deformed polytope institut fourier b p 74 38402 saint martin d heres cedex france e mail address mbrion fourier ujf grenoble fr ecole normale superieure 45 rue d ulm 75005 paris cedex 05 france e mail address vergne dmi ens fr

random polynomials with prescribed newton polytope the newton polytope pf of a polynomial f is well known to have a strong impact on its zeros as in the kouchnirenko bernstein theorem on the number of simultaneous zeros of m polynomials with given newton polytopes in this article we show that pf also has a strong impact on the distribution of zeros of one or several polynomials we equip the space of holomorphic polynomials of degreen in m complex variables with its usual su m 1 invariant gaussian measure and then consider the conditional measures np induced on the subspace of polynomials whose newton polytope pfnp when p the unit simplex then it is obvious and well known that the expected distribution of zeros zf1 fk regarded as a current of k polynomials f1 fk of degree n is uniform relative to the fubini study form our main results concern the conditional expectation e np zf1 fk of zeros of k polynomials with newton polytope npnp where p deg p these results are asymptotic as the scaling factor n 1 we show that e np zf1 fk is asymptotically uniform on the inverse image ap of the open scaled polytope 1 p via the moment map cp m for projective space however the zeros have an exotic distribution outside of ap and when k m the case of the kouchnirenko bernstein theorem the percentage of zeros outside ap approaches 0 as n 1

non parametric analysis of covariance an analysis of covariance model where the covariate effect is assumed only to be smooth is considered the possibility of different shapes of covariate effect in different groups is also allowed and tests of equality and of parallelism across groups are constructed these are implemented using gasser maller smoothing whose properties enable problems of bias to be avoided accurate moment based approximations are available for the distribution of each test statistic some data on spanish onions are used to contrast the non parametric approach with that of a nonlinear but parametric model a simulation study is also used to explore the properties of the non parametric tests

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

algebraic birkhoff factorization and the euler maclaurin formula on cones we equip the space of lattice cones with a coproduct which makes it a cograded coaugmented connnected coalgebra the exponential generating sum and exponential generating integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero we investigate the subdivision properties reminiscent of the inclusion exclusion principle for the cardinal on finite sets of such linear maps and show that these properties are compatible with the convolution quotient of maps on the coalgebra implementing the algebraic birkhoff factorization procedure on the linear maps under consideration we factorize the exponential generating sum as a convolution quotient of two maps with each of the maps in the factorization satisfying a subdivision property a direct computation shows that the polar decomposition of the exponential generating sum on a smooth lattice cone yields an euler maclaurin formula the compatibility with subdivisions of the convolution quotient arising in the algebraic birkhoff factorization then yields the euler maclaurin formula for any lattice cone this provides a simple formula for the interpolating factor by means of a projection formula

fully nonlinear neumann type boundary conditions for first order hamilton jacobi equations we consider problems of the following type h x u u 0 in where is a smooth bounded open set in r n u is a scalar function from into r u denotes its frechet differential at x and h is a given continuous function on xr r n this equation is nothing but a general form of the classical first order hamilton jacobi equation in order to investigate existence and uniqueness questions the equation has to be complemented with a boundary condition on or on a part of we consider here for reasons described below a fully nonlinear boundary condition of the form f x u u 0 on that we describe as being of the neumann type

a mathematical modeling for the lookback option with jump diffusion using binomial tree method abstract the binomial tree method btm first proposed by cox et al 1979 4 in diffusion models and extended by amin 1993 9 to jump diffusion models is one of the most popular approaches to pricing options in this paper we present a binomial tree method for lookback options in jump diffusion models and show its equivalence to certain explicit difference scheme we also prove the existence and convergence of the optimal exercise boundary in the binomial tree approximation to american lookback options and give the terminal value of the genuine exercise boundary further numerical simulations are performed to illustrate the theoretical results

on the rate of convergence of the binomial tree scheme for american options an american put option can be modelled as a variational inequality with a penalization approximation to this variational inequality the convergence rate o big delta x 2 3 big of the binomial tree scheme is obtained in this paper

a semi lagrangian approach for american asian options under jump diffusion a semi lagrangian method is presented to price continuously observed fixed strike asian options at each timestep a set of one dimensional partial integrodifferential equations pides is solved and the solution of each pide is updated using semi lagrangian timestepping crank nicolson and second order backward differencing timestepping schemes are studied monotonicity and stability results are derived with low volatility values it is observed that the nonsmoothness at the strike in the payoff affects the convergence rate a subquadratic convergence rate is observed

convergence of the trinomial tree method for pricing european american options in this paper we present a trinomial tree method for pricing options and show its equivalence to certain explicit difference scheme using the numerical analysis and the notion of viscosity solution we prove the uniform convergence of the trinomial tree method for european american options the accuracy and efficiency are shown through numerical simulations

special values of partial zeta functions of real quadratic fields at nonpositive integers and the euler maclaurin formula we compute the special values at nonpositive integers of the partial zeta function of an ideal of a real quadratic field applying an asymptotic version of euler maclaurin formula to the lattice cone associated to the ideal considered the euler maclaurin formula in volved is obtained by applying the todd series of differential opera tors to an integral of a small perturbation of the cone the additive property of todd series w r t the cone decomposition enables us to express the partial zeta values in terms of the continued fraction of the reduced element of the ideal the expression obtained uses the positive continued fraction which yields a virtual decomposition of the cone we apply the expression to some indexed families of real quadratic fields satisfying certain condition on the shape of the continued frac tions the families considered include those appeared in 20 and 21 as well as the richaud degert types we show that the partial zeta values at a given nonpositive integerk in the family indexed by n is a polynomial of n finally we compute explicitly the polynomials producing the par tial zeta values at s k for small k of some chosen families and compare these with some previously known results

new polytope decompositions and euler maclaurin formulas for simple integral polytopes abstract we give new weighted decompositions for simple polytopes generalizing previous results of lawrence varchenko and brianchon gram we start with witten s non abelian localization principle in equivariant cohomology for the norm square of the moment map in the context of toric varieties to obtain a decomposition for delzant polytopes then by a purely combinatorial argument we show that this formula holds for any simple polytope as an application we study euler maclaurin formulas

checking for lack of fit in linear models with parametric variance functions i adapt near replicate lack of fit tests for checking the adequacy of a linear model for means to check for lack of fit in a standard log linear model for variances a graphical method for checking lack of fit in the variance model is also proposed in addition an overall test of lack of fit in means or variances is presented three examples are used to illustrate the techniques

how to integrate a polynomial over a simplex this paper starts by settling the computational complexity of the problem of integrating a polynomial function f over a rational simplex we prove that the problem is np hard for arbitrary polynomials via a generalization of a theorem of motzkin and straus on the other hand if the polynomial depends only on a fixed number of variables while its degree and the dimension of the simplex are allowed to vary we prove that integration can be done in polynomial time as a consequence for polynomials of fixed total degree there is a polynomial time algorithm as well we explore our algorithms with some experiments we conclude the article with extensions to other polytopes and discussion of other available methods 1

asymptotic euler maclaurin formula over lattice polytopes abstract formulas for the riemann sums over lattice polytopes determined by the lattice points in the polytopes are often called euler maclaurin formulas an asymptotic euler maclaurin formula by which we mean an asymptotic expansion formula for riemann sums over lattice polytopes was first obtained by guillemin and sternberg 2007 11 then the problem is to find a concrete formula for each term of the expansion in this paper an asymptotic euler maclaurin formula of the riemann sums over general lattice polytopes is given the formula given here is an asymptotic form of the so called local euler maclaurin formula of berline and vergne 2007 3 for delzant polytopes our proof given here is independent of the local euler maclaurin formula furthermore a concrete description of differential operators which appear in each term of the asymptotic expansion for delzant lattice polytopes is given by using this description when the polytopes are delzant lattice a concrete formula for each term of the expansion in two dimension and a formula for the third term of the expansion in arbitrary dimension are given

computing the ehrhart quasi polynomial of a rational simplex we present a polynomial time algorithm to compute any fixed number of the highest coefficients of the ehrhart quasi polynomial of a rational simplex previously such algorithms were known for integer simplices and for rational polytopes of a fixed dimension the algorithm is based on the formula relating the kth coefficient of the ehrhart quasi polynomial of a rational polytope to volumes of sections of the polytope by affine lattice subspaces parallel to k dimensional faces of the polytope we discuss possible extensions and open questions

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

diagnostics for heteroscedasticity in regression summary for the usual regression model without replication we provide a diagnostic test for heteroscedasticity based on the score statistic a graphical procedure to complement the score test is also presented some key u ords influence linear model residual score test diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions the recent literature on diagnostics is dominated by studies of methods for the detection of influential observations cook weisberg 1982 provide a review diagnostics for the relevance of specific assumptions however have not received the same degree of attention even though these may be of equal importance our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present available methods for studying this assumption include both graphical and nongraphical procedures the usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable a megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa weisberg 1980 chapter 6 in 3 we suggest several ways in which this

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

euler maclaurin with remainder for a simple integral polytope we give an euler maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope we prove this formula by elementary methods

applying greek letters to robust option price modeling by binomial tree abstract in this paper a new model is proposed for pricing a european option using the binomial tree method in conjunction with the greek letters in the proposed method the covariance matrix of high and low stock prices was calculated in an uncertainty region applying robust option pricing model an interval of prices instead of spot prices for an option was obtained greek letters were incorporated into a robust option model to ameliorate the accuracy of the interval price it was found out that the interval prices obtained by the present model were flexible with increased accuracy compared with those obtained by the robust option using the binomial tree model it is also indicated that the advantage of the present model over existing models is more tangible in the event of out of the money call option furthermore the accuracy improvement was found to be less noticeable when the maximum costs were equal to each other

variance function estimation in regression the effect of estimating the mean abstract the authors consider estimation of a variance function g in regression problems such estimation requires simultaneous estimation of the mean function f we obtain sharp results on the extent to which the smoothness of f influences best rates of convergence for estimating g for example in nonparametric regression with two derivatives on g classical rates of convergence are possible if and only if the unknown f satisfies a lipschitz condition of order 1 3 or more if a parametric model is known for g then g may be estimated n 1 2 consistently if and only if f is lipschitz of order 1 2 or more optimal rates of convergence are attained by kernel estimators

asymptotically efficient estimation of a nonlinear model of the heteroscedasticity and the calibration of measurement systems the measurement system calibration includes the estimation of the sensor error models in order to get an optimal estimation of the measured parameters the paper is devoted to the estimation of a nonlinear parametric model of the heteroscedasticity and its application to the calibration of measurement systems the heteroscedasticity occurs in regression when the measurement noise variance is nonconstant the maximum likelihood ml estimation of variance function parameters leads to a system of nonlinear equations the iterative solution of these nonlinear equations is based entirely on a successful choice of initial conditions which is intractable in practice to overcome this difficulty another linear quasi ml estimator is proposed it is strongly consistent asymptotically gaussian and only slightly less efficient than the cramer rao lower bound by using this estimator as an initial condition an asymptotically efficient estimation is obtained by using one step noniterative newton method the theoretical findings have been applied to the calibration of the egnos gps positioning algorithm in the sub urban environments

model checking techniques for linear models with parametric variance functions we present graphical and numerical methods for assessing the adequacy of the log linear model for variances the proposed methods are derived from the cumulative sum of residuals over the covariate or linear predictor under the assumed model the cumulative residual process converges weakly to a 0 mean gaussian process whose distribution can be approximated via monte carlo simulation the observed cumulative residual pattern can then be compared both visually and analytically to a number of simulated realizations from the approximate null distribution these comparisons enable one to examine the functional form of each covariate the link function as well as the overall model adequacy of the variance model simulation studies demonstrate that the proposed methods perform well in practical settings illustrations with three datasets are provided

the euler maclaurin formula for simple integral polytopes we give a euler maclaurin formula with remainder for the sum of a smooth function on the integral points in a simple integral lattice polytope our proof uses elementary methods

optimal control on the l infty norm of a diffusion process stochastic control problems are considered where the cost to be minimized is either a running maximum of the state variable or more generally a running maximum of a function of the state variable and the control in both cases it is proved that the value function which must be defined on an augmented state space to take care of the non markovian feature of the running maximum is the unique viscosity solution of the associated bellman equation which turns out to be in the second case a variational inequality with an oblique derivative boundary condition most of this work consists of proving the convergence of lp approximations and this is done by purely partial differential equation pde methods

the ehrhart polynomial of a lattice polytope the problem of counting the number of lattice points inside a convex lattice polytope in r a polytope whose vertices have integer coordinates has been studied from a variety of perspectives here we use the poisson summation formula and related techniques in fourier analysis to obtain a formula for the number of lattice points inside all integral dilates of a lattice polytope we show that an associated generating function has an explicit representation in terms of sums of cotangents which are higher dimensional generalizations of dedekind sums let en denote the n dimensional integer lattice in r and let p be an n dimensional lattice polytope in r which is a compact simplicial complex of pure dimension n whose vertices lie on the lattice consider the function of an integer valued variable t that describes the number of lattice points that lie inside the dilated polytope tp

characteristic classes of singular toric varieties in this paper we compute the motivic chern classes and homology hirzebruch characteristic classes of possibly singular toric varieties which in the context of complete toric varieties fit nicely with a generalized hirzebruch riemann roch theorem as important special cases we obtain new or recover well known formulae for the baum fulton macpherson todd or macpherson s chern classes of toric varieties as well as for the thom milnor l classes of simplicial projective toric varieties we present two different perspectives for the computation of these characteristic classes of toric varieties first we take advantage of the torus orbit decomposition and the motivic properties of the motivic chern and respectively homology hirzebruch classes to express the latter in terms of dualizing sheaves and respectively the dual todd classes of closures of orbits this method even applies to torus invariant subspaces of a given toric variety the obtained formula is then applied to weighted lattice point counting in lattice polytopes and their subcomplexes yielding generalized pick type formulae second in the case of simplicial toric varieties we compute our characteristic classes by using the lefschetz riemann roch theorem of edidin graham in the context of the geometric quotient description of such varieties in this setting we define mock hirzebruch classes of simplicial toric varieties which specialize to the mock chern mock todd and mock l classes of such varieties and investigate the difference between the actual homology hirzebruch class and the mock hirzebruch class we show that this difference is localized on the singular locus and we obtain a formula for it in which the contribution of each singular cone is identified explicitly finally the two methods of computing characteristic classes are combined for proving several characteristic class formulae originally obtained by cappell and shaneson in the early 1990s 2015 wiley periodicals inc

numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers in this paper we study different algorithms for reflected backward stochastic differential equations bsde in short with two continuous barriers based on the framework of using a binomial tree to simulate 1 d brownian motion we introduce numerical algorithms by the penalization method and the reflected method respectively in the end simulation results are also presented

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

convergence of the binomial tree method for american options in a jump diffusion model the paper studies the binomial tree method for american options in a jump diffusion model we employ the theory of viscosity solution to show uniform convergence of the binomial tree method for american options we also prove existence and convergence of the optimal exercise boundary in the binomial tree approximation in addition the terminal value of the optimal exercise boundary is given for american options in jump diffusion models

on a semiparametric variance function model and a test for heteroscedasticity we propose a general semiparametric variance function model in a fixed design regression setting in this model the regression function is assumed to be smooth and is modelled nonparametrically whereas the relation between the variance and the mean regression function is assumed to follow a generalized linear model almost all variance function models that were considered in the literature emerge as special cases least squares type estimates for the parameters of this model and the simultaneous estimation of the unknown regression and variance functions by means of nonparametric kernel estimates are combined to infer the parametric and nonparametric components of the proposed model the asymptotic distribution of the parameter estimates is derived and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model this result is applied to obtain a data based test for heteroscedasticity under minimal assumptions on the shape of the regression function

wall crossings for double hurwitz numbers abstract double hurwitz numbers count covers of p 1 by genus g curves with assigned ramification profiles over 0 and and simple ramification over a fixed branch divisor goulden jackson and vakil have shown double hurwitz numbers are piecewise polynomial in the orders of ramification goulden et al 2005 10 and shadrin shapiro and vainshtein have determined the chamber structure and wall crossing formulas for g 0 shadrin et al 2008 15 this paper gives a unified approach to these results and strengthens them in several ways the most important being the extension of the results of shadrin et al 2008 15 to arbitrary genus the main tool is the authors previous work cavalieri et al 2010 6 expressing double hurwitz number as a sum over certain labeled graphs we identify the labels of the graphs with lattice points in the chambers of certain hyperplane arrangements which give rise to piecewise polynomial functions our understanding of the wall crossing for these functions builds on the work of varchenko 1987 17 and could have broader applications