uniqueness results for the one dimensional p laplacian this paper is concerned with positive solutions of the boundary value problem y p 2y f y 0 y b 0 y b where p 1 b is a positive parameter assume that f is continuous on 0 changes sign from nonpositive to positive and f y yp 1 is nondecreasing in the interval of f 0 the uniqueness results are proved using a time mapping analysis

a hybrid monte carlo acceleration method of pricing basket options based on splitting abstract pricing basket options has always been one of the key problems in financial engineering because of high dimensionality and low convergence rate this paper proposes a hybrid monte carlo variance reduction method for pricing basket options first by splitting the payoff of the basket option into two parts we can price basket options by value the two parts respectively the first part has a closed form expectation formula the second part can be considered as a small probability event to reduce variance for simulating the second part the conditional monte carlo cmc method combined with the importance sampling is method is adapted because these two methods are all effective to deal with small probability events for is method it is a challenge to compute the optimal parameters with as little computational cost as possible therefore an efficient prediction correction pc iteration algorithm based on moment estimation is proposed to determine the optimal parameters in the importance sampling method some theoretical analyses for the existence and uniqueness of the optimal parameters in the is method and the convergence of the pc method are also given numerical results show that the hybrid variance reduction method has great variance reduction effect and pc iteration algorithm can save a lot of computing costs comparing with the traditional newton s iteration method

exact multiplicity results for a class of two point boundary value problems abstract this paper is concerned with the exact number of positive solutions for boundary value problems y p 2 y f y 0 and y 1 y 1 0 where p 1 and 0 is a positive parameter we consider the case in which the nonlinearity f is positive on 0 and p 1 f u u f u changes sign from negative to positive

uniqueness of positive radial solutions of δu f u 0 in ℝ n ii we prove a uniqueness result for the positive solution of u f u 0 in r n which goes to 0 at the result applies to a wide class of nonlinear functions f including the important model case f u u u p 1 p n 2 n 2 the result is proved by reducing to an initial boundary problem for the ode u n 1 r f u 0 and using a shooting method

exact multiplicity for degenerate two point boundary value problems with p convex nonlinearity the exact number of positive solutions of a degenerate quasilinear two point boundary value problem is investigated for the generalization of earlier results concerning the nondegenerate case with convex nonlinearity suitably defined p convex nonlinearities are considered strictly p convex c2 functions having a non negative root are classified according to the shape of the bifurcation diagram of positive solutions versus the length of the interval we have uniqueness when f 0 0 and 0 1 or 2 solutions when f 0 0 similarly to the non degenerate case provided that the number of solutions is finite however now there may also occur a continuum of solutions connected to a dead core type phenomenon the proof of our results relies on the shooting method for the characterization of the shape of the time map in contrast to the non degenerate case the shooting method does not determine directly the number of solutions owing to the lack of uniqueness of the corresponding ivp exact conditions on the uniqueness of the ivp and in the case of non uniqueness the number and types of its local solutions are given based on this all the positive solutions of the bvp can be compiled

efficient basket monte carlo option pricing via a simple analytical approximation we present a new valuation method for basket options that is based on a limiting approximation of the arithmetic mean by the geometric mean using this approximation combined with a new analytical pricing formula for an approximating geometric mean based option as a control variate excellent performance for monte carlo pricing in a control variate setting is obtained

exact number of positive solutions for semipositone problems this paper is concerned with the exact number of positive solutions for the boundary value problem y p 2y f y 0 and y 1 y 1 0 where p 1 and 0 is a positive parameter we consider the case in which both f u and g u p 1 f u uf u change sign exactly once from negative to positive on 0

positive solutions of elliptic equations involving supercritical growth positive radial solutions of elliptic equation involving supercritical growth are analysed as their supremum norm tends to infinity it is shown that they converge uniformly away from the origin as well as in h 1 to the unique singular solution

space time adaptive finite difference method for european multi asset options the multi dimensional black scholes equation is solved numerically for a european call basket option using a priori a posteriori error estimates the equation is discretized by a finite difference method on a cartesian grid the grid is adjusted dynamically in space and time to satisfy a bound on the global error the discretization errors in each time step are estimated and weighted by the solution of the adjoint problem bounds on the local errors and the adjoint solution are obtained by the maximum principle for parabolic equations comparisons are made with monte carlo and quasi monte carlo methods in one dimension and the performance of the method is illustrated by examples in one two and three dimensions

quasi monte carlo methods in numerical finance this paper introduces and illustrates a new version of the monte carlo method that has attractive properties for the numerical valuation of derivatives the traditional monte carlo method has proven to be a powerful and flexible tool for many types of derivatives calculations under the conventional approach pseudo random numbers are used to evaluate the expression of interest unfortunately the use of pseudo random numbers yields an error bound that is probabilistic which can be a disadvantage another drawback of the standard approach is that many simulations may be required to obtain a high level of accuracy there are several ways to improve the convergence of the standard method this paper suggests a new approach which promises to be very useful for applications in finance quasi monte carlo methods use sequences that are deterministic instead of random these sequences improve convergence and give rise to deterministic error bounds the method is explained and illustrated with several examples these examples include complex derivatives such as basket options asian options and energy swaps

the equivalence problem for single valued two way transducers on npdtol languages is decidable the equivalence problem for deterministic two way transducers was a longstanding problem finally shown decidable by e m gurari we show a generalization of this result namely that it is decidable whether two single valued two way transducers are equivalent on an npdtol language we obtain this result by showing that it is even decidable whether a two way transducer is single valued on an npdtol language our solution is based on the compactness property of the systems of equations over a finitely generated free monoid shown recently by j lawrence and m albert and also v s guba this was a longstanding open problem known as the ehrenfeucht conjecture our approach also shows that for one way transducers their single valuedness on a given hdtol language can be tested and thus the equivalence of two single valued one way transducers on an hdtol language is decidable too our results imply the decidability of the hdol and hdtol sequence equivalence problems also longstanding open problems solved rece

on the monotonicity of the time map the equation au y u y 0 on the unit ball with homogeneous linear boundary conditions has been much studied cf 1 2 and the references therein the change of variable x l i transforms this equation to mx a 0 1x1 r 1 1 where r fi for radial solutions of this equation lying in say the kth nodal class r depends only on p u o r t p this function which describes how the size of the balls on which radial solutions exist vary with the quantity u o turns out to be an important function determining much of the behavior of the solutions thus if we consider 1 1 together with the boundary conditions cu x i du x dn 0 1x1 r

the positive solutions of boundary value problems for a class of one dimensional p laplacians abstract this paper is concerned with the exact number of positive solutions for boundary value problems u p 2 u f u 0 and u 1 u 1 0 where p 1 and 0 is a positive parameter we consider the case in which the nonlinearity f changes sign from positive to negative on 0 for example f u u u where

the equivalence problem for deterministic two way sequential transducers is decidable the equivalence problem for deterministic two way sequential transducers is a long time open problem which is known to be decidable for some restricted cases here the problem is shown to be decidable also for the general case in fact the result holds even when the devices are allowed to make some finite number of nondeterministic moves

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

normality and two way automata we prove that two way transducers both deterministic and non deterministic cannot compress normal numbers to achieve this we first show that it is possible to generalize compressibility from one way transducers to two way transducers these results extend a known result normal infinite words are exactly those that cannot be compressed by lossless finite state transducers and more generally by bounded to one non deterministic finite state transducers we also argue that such a generalization cannot be extended to two way transducers with unbounded memory even in the simple form of a single counter

on the stability properties of nonnegative solutions of semilinear problems with convex or concave nonlinearity 497 abstract we investigate the stability of nontrivial nonnegative stationary solutions of semilinear initial boundary value problems with convex or concave nonlinearity in the convex case f 0 0 implies instability in the concave case f 0 0 implies stability we also discuss the necessity of the sign condition on f 0

positive solution curves of semipositone problems with concave nonlinearities we consider the positive solutions to the semilinear equation where denotes a smooth bounded region in n n 1 and 0 here f 0 is assumed to be monotonically increasing concave and such that f 0 f lim t f t 0 we establish the stability and uniqueness of large positive solutions in terms of f t t when is a ball we determine the exact number of positive solutions for each 0 we also obtain the geometry of the branches of positive solutions completely and establish how they evolve this work extends and complements that of 3 7 where f 0

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

bifurcation phenomena associated to the p laplace operator on determine la structure de l ensemble des solutions u de u x p 2 u x x f u u p 2 u sur 0 1 telles que u 0 u 1 0 ou p 1 et r on demontre que les solutions avec k zeros sont uniques quand 1 2

on certain second order ordinary differential equations associated with sobolev poincare type inequalities on considere l equation e i 1 n u x i p 2 u x i x i u q 2 u 0 dans u x 0 sur on donne les proprietes des solutions de e pour le cas n 1 et a b mais pour p q 1 avec p q regularite existence et unicite de solutions positives

instability of nonnegative solutions for a class of semilinear abstract we consider the boundary value problem u x f u x x bu x 0 x where is a bounded region in rn with smooth boundary bu x h x u 1 u n where 0 1 h r with h 1 when 1 0 f is a smooth function such that u 0 for u 0 u for u 0 and u 0 for u for some 0 we provide a simple proof to establish that every non trivial nonnegative solution is unstable

multi dimensional option pricing using radial basis functions and the generalized fourier transform we show that the generalized fourier transform can be used for reducing the computational cost and memory requirements of radial basis function methods for multi dimensional option pricing we derive a general algorithm including a transformation of the black scholes equation into the heat equation that can be used in any number of dimensions numerical experiments in two and three dimensions show that the gain is substantial even for small problem sizes furthermore the gain increases with the number of dimensions