follmer schweizer decomposition and mean variance hedging for general claims let x be an r d valued special semimartingale on a probability space f f t 0 t t p with decomposition x x 0 m a and the space of all predictable x integrable processes such that dx is in the space s 2 of semimartingales if h is a random variable in l 2 we prove under additional assumptions on the process x that h can be written as the sum of an f 0 measurable random variable h 0 a stochastic integral of x and a martingale part orthogonal to m moreover this decomposition is unique and the function mapping h with its decomposition is continuous with respect to the l 2 norm finally we deduce from this continuity that the subspace of l 2 generated by dx where is closed in l 2 and we give some applications of this result to financial mathematics

convergence rates of moving mesh methods for moving boundary partial integro differential equations from regime switching jump diffusion asian option pricing abstract this paper studies the convergence rates of moving mesh methods for a system of moving boundary partial integro differential equations pides which arise in the asian option pricing under the state dependent regime switching jump diffusion models the value function of the asian option under the model is governed by a system of two dimensional pides in this paper the two dimensional pides are recast into a one dimensional moving boundary problem of the pides a moving finite difference method fdm is proposed to solve the one dimensional moving boundary problem and the convergence rates are proved numerical examples are provided to confirm the theoretical results

a new efficient numerical method for solving american option under regime switching model a system of coupled free boundary problems describing american put option pricing under regime switching is considered in order to build numerical solution firstly a front fixing transformation is applied transformed problem is posed on multidimensional fixed domain and is solved by explicit finite difference method the numerical scheme is conditionally stable and is consistent with the first order in time and second order in space the proposed approach allows the computation not only of the option price but also of the optimal stopping boundary numerical examples demonstrate efficiency and accuracy of the proposed method the results are compared with other known approaches to show its competitiveness

methods for pricing american options under regime switching we analyze a number of techniques for pricing american options under a regime switching stochastic process the techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable in the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations numerical tests indicate that a fixed point policy iteration coupled with a direct control formulation is a reliable general purpose method finally we remark that we formulate the american problem as an abstract optimal control problem hence our results are applicable to more general problems as well

shimura invariant differential operators and their eigenvalues let bar d be the covariant cauchy riemann operator and mathcal d the covariant holomorphic differential operator on a line bundle over a hermitian symmetric space g k we study the shimura invariant differential operators defined via bar d and mathcal d we find the eigenvalues of a family of the shimura operators and of the generators

soft input soft output equalizers for turbo receivers a statistical physics perspective many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations i e the inference problem as well as with the problem of estimating the model parameters such an inference and estimation problem is encountered for example in adaptive turbo equalization demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty given the received signal samples and a priori information provided by the decoder an exact inference algorithm computes the a posteriori probability app values for all transmitted symbols but the computation of app s is known to be an np hard problem thus rendering this approach computationally prohibitive in most cases we show in this paper how may of the well known low complexity soft input soft output siso equalizers including the channel matched filter based linear siso equalizers and minimum mean square error mmse siso equalizers as well as the expectation maximization em algorithm based siso demodulators in the presence of the rayleigh fading channel can be formulated as solutons to a variational optimization problem the variational optimization is a well established methodology for low complexity inference and estimation originating from statistical physics importantly the imposed variational optimization framework provides an interesting link between the app demodulators and the linear siso equalizers moreover it provides a new set of insights into the structure and performance of these widely celebrated linear siso equalizers while suggesting some fine tuning of them as well

w gauge structures and their anomalies an algebraic approach starting from flat two dimensional gauge potentials we propose the notion of w gauge structure in terms of a nilpotent becchi rouet stora brs differential algebra the decomposition of the underlying lie algebra with respect to an sl 2 subalgebra is crucial for the discussion of conformal covariance in particular the appearance of a projective connection different sl 2 embeddings lead to different w gauge structures we present a general soldering procedure which allows one to express zero curvature conditions for the w currents in terms of conformally covariant differential operators acting on the w gauge fields and to obtain at the same time the complete nilpotent brs differential algebra generated by w currents gauge fields and the ghost fields corresponding to w diffeomorphisms as illustrations we treat the cases of sl 2 itself and the two different sl 2 embeddings in sl 3 viz the w 1 3 and w 2 3 gauge structures in some detail in these cases we determine algebraically w anomalie

a dominance based soft input soft output mimo detector with near optimal performance iterative detection and decoding for multi input multi output mimo communication systems require a soft input soft output siso detection algorithm which in the optimal formulation is well known to be exponentially complex in the number of transmitting antennas this paper presents a novel siso detector for mimo systems named siso king decoder it is a tree search branch and bound algorithm which exploits the properties of the channel matrix and the a priori information on the transmitted bits to reduce the overall computational complexity the proposed algorithm is compared with the siso single tree search sphere decoder 1 simulation results are provided to show the complexity reduction without relevant performance loss in terms of bit error rate

partial marginalization soft mimo detection with higher order constellations a new method for multiple input multiple output mimo detection with soft output the partial marginalization pm algorithm was recently proposed advantages of the method are that it is straightforward to parallelize and that it offers a fully predictable runtime pm trades performance for computational complexity via a user defined parameter in the limit of high computational complexity the algorithm becomes the map demodulator the pm algorithm also works with soft input but until now it has been unclear how to apply it for other modulation formats than binary phase shift keying bpsk per real dimension in this correspondence we explain how to extend pm with soft input to general signaling constellations while maintaining the low complexity advantage of the original algorithm

generalized bernstein reznikov integrals we find a closed formula for the triple integral on spheres in mathbb r 2n times mathbb r 2n times mathbb r 2n whose kernel is given by powers of the standard symplectic form this gives a new proof to the bernstein reznikov integral formula in the n 1 case our method also applies for linear and conformal structures

computing american option price under regime switching with rationality parameter american put option pricing under regime switching is modelled by a system of coupled partial differential equations the proposed model combines better the reality of the market by incorporating the regime switching jointly with the emotional behaviour of traders using the rationality parameter approach recently introduced by tagholt gad and lund petersen to cope with possible irrational exercise policy the classical rational exercise is recovered as a limit case of the rational parameter the resulting nonlinear system of pdes is solved by a weighted finite difference method also known as method in order to avoid the need of an iterative method for nonlinear system the term with rationality parameter and the coupling term are treated explicitly next the resulting linear system is solved by thomas algorithm stability conditions for the numerical scheme are studied by using von neumann approach numerical examples illustrate the efficiency and accuracy of the proposed method

hybrid laplace transform and finite difference methods for pricing american options under complex models abstract in this paper we propose a hybrid laplace transform and finite difference method to price finite maturity american options which is applicable to a wide variety of asset price models including the constant elasticity of variance cev hyper exponential jump diffusion hejd markov regime switching models and the finite moment log stable fmls models we first apply laplace transforms to free boundary partial differential equations pdes or fractional partial differential equations fpdes governing the american option prices with respect to time and obtain second order ordinary differential equations odes or fractional differential equations fdes with free boundary which is named as the early exercise boundary in the american option pricing then we develop an iterative algorithm based on finite difference methods to solve the odes or fdes together with the unknown free boundary values in the laplace space both the early exercise boundary and the prices of american options are recovered through inverse laplace transforms numerical examples demonstrate the accuracy and efficiency of the method in cev hejd markov regime switching models and the fmls models

becchi rouet stora cohomology of zero curvature systems ii the noncomplete ladder case the yang mills type theories and their brs cohomologies are analyzed within the zero curvature formalism

w algebras from canonical transformations it is shown how w algebras emerge from very peculiar canonical transformations with respect to the canonical symplectic structure on a compact riemann surface the action of smooth diffeomorphisms of the cotangent bundle on suitable generating functions is written in the brs framework while a w symmetry is exhibited subsequently the complex structure of the symmetry spaces is studied and the related brs properties are discussed the specific example of the so called w3 algebra is treated in relation to some other different approaches

rankin cohen brackets transvectants and covariant differential operators we give a geometric construction of the transvectant on a hermitian symmetric space which in the case of the unit disk is also called the rankin cohen bracket in terms of the covariant differentiation

a new simple tree approach for the heston s stochastic volatility model abstract we present a new tree based numerical approach for options pricing under heston s stochastic volatility model the tree approach is simple to implement computationally cheap and has a very clear financial interpretation in addition we build an equivalence between our tree method and an explicit finite difference method for the heston model based on our tree approach such an equivalence is proven analytically and verified numerically the numerical performance shows that our tree is robust and provides accurate results within very short computing time

subspace beamforming for near capacity mimo performance a subspace beamforming method is presented that decomposes a multiple input multiple output mimo channel into multiple pairs of subchannels the pairing is done based on singular values such that similar channel capacity is obtained between different subchannel pairs this new capacity balancing concept is key to achieving high performance with low complexity we apply the subspace idea to geometric mean decomposition gmd and maximum likelihood ml detection the proposed subspace gmd scheme requires only two layers of detection decoding regardless of the total number of subchannels thus alleviating the latency issue associated with conventional gmd we also show how the subspace concept makes the optimization of ml beamforming and ml detection itself feasible for any k timesk mimo system simulation results show that subspace beamforming performs nearly as well as optimum gmd performance and to within only a few decibels of the shannon bound

a stochastic control approach to the pricing of options we construct a stochastic control model of a portfolio in which the investor may invest in stock call options on the stock or risk free bonds he may also borrow funds we assume that the investor is attempting to maximize expected utility of total wealth at expiration of the options where the utility function is given as wealth to the power 0 1 this includes both the risk averse and risk neutral cases we allow the borrowing interest rate r to be distinct from the lending interest rate r we make two fundamental assumptions i the investor cannot achieve infinite expected utility of wealth in finite time stable markets and ii the market will set the option price to minimize the investor s maximal expected utility of wealth i e options are priced using a minimax strategy the market is stable only when r r we prove in the case r r and 1 that the minimax european call option price ft s is given as the solution of the black scholes equation ft i i 2s2fss i s fs i f 0 where i r when r i 2 1 i r when i 2 1 r and i i 2 1 if r i 2 1 r the parameter is the stock return drift and i is the stock return diffusion if r r then the call option price must by stable markets always be the black scholes price with rate r in the risk neutral 1 case we must have r r for a stable market and the option price given by the black scholes equation but with i explicit solutions are presented and the optimal portfolios and returns are also derived comparable results are obtained for american call options which can be exercised at any time up to and including the expiration date in this case the option pricing function is shown to be the solution of an obstacle problem

on a class of nearly holomorphic automorphic forms with a b 1 e c and 0 n e z the point that attracts our attention is its nonholomorphic nature it is noteworthy that f is holomorphic if k 2 and also such nonholomorphy doesn t appear in the hilbert modular case therefore one may naturally ask whether this is an isolated oddity in our previous papers 10 and 13 we showed that it was not so in fact a similar eisenstein series on sp n q or on su n n of a particular weight can have the form

approximating random variables by stochastic integrals let x be a semimartingale and the space of all predictable x integrable processes such that dx is in the space 2 of semimartingales we consider the problem of approximating a given random variable h l 2 by a stochastic integral 0 t s dx s with respect to the l 2 norm if x is special and has the form x x 0 m d we construct a solution in feedback form under the assumptions that 2 d is deterministic and that h admits a strong f s decomposition into a constant a stochastic integral of x and a martingale part orthogonal to m we provide sufficient conditions for the existence of such a decomposition and we give several applications to quadratic optimization problems arising in financial mathematics

a high order finite element scheme for pricing options under regime switching jump diffusion processes this paper considers the numerical pricing of european american and butterfly options whose asset price dynamics follow the regime switching jump diffusion process in an incomplete market structure and using the no arbitrage pricing principle the option pricing problem under the jump modulated regime switching process is formulated as a set of coupled partial integro differential equations describing different states of a markov chain we develop efficient numerical algorithms to approximate the spatial terms of the option pricing equations using linear and quadratic basis polynomial approximations and solve the resulting initial value problem using exponential time integration various numerical examples are given to demonstrate the superiority of our computational scheme with higher level of accuracy and faster convergence compared to existing methods for pricing options under the regime switching model

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

tensor products of holomorphic representations and bilinear differential operators let h be the weighted bergman space on a bounded symmetric domain d g k it has analytic continuation in the weight and for in the so called wallach set h still forms unitary irreducible projective representations of g we give the irreducible decomposition of the tensor product h 1 h 2 of the representations for any two unitary weights and we find the highest weight vectors of the irreducible components we find also certain bilinear differential intertwining operators realizing the decomposition and they generalize the classical transvectants in invariant theory of sl 2 c as applications we find a generalization of the bol s lemma and we characterize the multiplication operators by the coordinate functions on the quotient space of the tensor product h 1 h 2 modulo the subspace of functions vanishing of certain degree on the diagonal

a near maximum likelihood decoding algorithm for mimo systems based on semi definite programming in multiple input multiple output mimo systems maximum likelihood ml decoding is equivalent to finding the closest lattice point in an n dimensional complex space in general this problem is known to be np hard in this paper a quasi ml algorithm based on semi definite programming sdp is proposed we introduce several sdp relaxation models for mimo systems with increasing complexity we use interior point methods for solving the models and obtain a near ml performance with polynomial computational complexity lattice basis reduction is applied to further reduce the computational complexity of solving these models the proposed relaxation models are also used for soft output decoding in mimo systems

a polyakov action on riemann surfaces ii we continue the model independent study of the polyakov action on an arbitrary compact surface without boundary of genus larger than 2 as the general solution of the relevant conformal ward identity a general formula for the polyakov action and an explicit calculation of the energy momentum tensor density is provided it is further shown how polyakov s sl 2 c symmetry emerges in a curved base surface

soft input soft output single tree search sphere decoding soft input soft output siso detection algorithms form the basis for iterative decoding the computational complexity of siso detection often poses significant challenges for practical receiver implementations in particular in the context of multiple input multiple output mimo wireless communication systems in this paper we present a low complexity siso sphere decoding algorithm based on the single tree search paradigm proposed originally for soft output mimo detection in studer soft output sphere decoding algorithms and vlsi implementation ieee j sel areas commun vol 26 no 2 pp 290 300 feb 2008 the new algorithm incorporates clipping of the extrinsic log likelihood ratios llrs into the tree search which results in significant complexity savings and allows to cover a large performance complexity tradeoff region by adjusting a single parameter furthermore we propose a new method for correcting approximate llrs resulting from sub optimal detectors which often significantly improves detection performance at low additional computational complexity

zero curvature conditions and conformal covariance two dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated the analysis is based on the kostant decomposition of simple lie algebras in terms of representations with respect to their principal sl 2 subalgebra

large chiral diffeomorphisms on riemann surfaces and w algebras the diffeomorphism action lifted on truncated chiral taylor expansion of a complex scalar field over a riemann surface is presented in the paper under the name of large diffeomorphisms after an heuristic approach we show how a linear truncation in the taylor expansion can generate an algebra of symmetry characterized by some structure functions such a linear truncation is explicitly realized by introducing the notion of forsyth frame over the riemann surface with the help of a conformally covariant algebraic differential equation the large chiral diffeomorphism action is then implemented through a becchi rouet stora brs formulation for a given order of truncation leading to a more algebraic setup in this context the ghost fields behave as holomorphically covariant jets subsequently the link with the so called w algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones we give a general solution with the help of the structure functions pertaining to al

matrix lifting semi definite programming for detection in multiple antenna systems this paper presents a computationally efficient decoder for multiple antenna systems the proposed algorithm can be used for any constellation qam or psk and any labeling method the decoder is based on matrix lifting semi definite programming sdp the strength of the proposed method lies in a new relaxation approach applied to the previous work by mobasher this results in a reduction of the number of variables from nk 1 nk 2 2 in the previous work by mobasher to 2n k 2 in the new method where n is twice the number of transmit antennas and k is the number of constellation points in each real dimension it is shown that this reduction in the number of variables results in a significant computational complexity reduction compared to the previous work by mobasher moreover the proposed method offers a better symbol error rate performance as compared to some known and recent sdp based quasi maximum likelihood detection methods reported in the literature

approximation pricing and the variance optimal martingale measure let x be a semimartingale and let be the space of all predictable x integrable processes v such that so dx is in the space s 2 of semi martingales we consider the problem of approximating a given random variable h l 2 p by the sum of a constant c and a stochastic integral s 0 t v s dx s with respect to the l 2 p norm this problem comes from financial mathematics where the optimal constant v 0 can be interpreted as an approximation price for the contingent claim h an elementary computation yields v 0 as the expectation of h under the variance optimal signed martingale measure p and this leads us to study p in more detail in the case of finite discrete time we explicitly construct p by backward recursion and we show that p is typically not a probability but only a signed measure in a continuous time framework the situation becomes rather different we prove that p is nonnegative if x has continuous paths and satisfies a very mild no arbitrage condition as an application we show how to obtain the optimal integrand in feedback form with the help of a backward stochastic differential equation

semidefinite relaxation approaches to soft mimo demodulation for higher order qam signaling the soft demodulator is a key component of receivers that employ iterative demodulation and decoding for multiple input multiple output systems with binary or qpsk signaling the semidefinite relaxation sdr approach to list based soft demodulation provides a desirable balance between the performance and computational cost in this paper that approach is extended to systems with higher order qam signaling for the class of list sdr demodulators the key to the extension is a quadratic approximation of the a priori information and for the more computationally efficient class of single sdr demodulators the key to the extension is an algebraic expression derived herein for the probability that the sdr randomization procedure generates each candidate symbol to implement these demodulators customized primal dual and dual scaling algorithms are developed to solve the underlying semidefinite programs the performance of the proposed demodulators is compared with that of some existing demodulators by using error rate simulations the empirical distribution of the computational cost and exit chart analyses in our comparisons the proposed single sdr demodulator provides performance that comes close to that of the list sequential demodulator at a computational cost that is close to that of the minimum mean square error parallel soft interference canceller

becchi rouet stora tyutin structure for the mixed weyl diffeomorphism residual symmetry in this paper we show the compatibility of the so called dressing field method which allows a systematic reduction of gauge symmetries with the inclusion of diffeomorphisms in the becchi rouet stora tyutin brst algebra of a gauge theory the robustness of the scheme is illustrated on two examples where cartan connections play a significant role the former is general relativity while the latter concerns the second order conformal structure where one ends up with a brst algebra handling both the weyl residual symmetry and diffeomorphisms of spacetime we thereby provide a geometric counterpart to the brst cohomological treatment used in boulanger j math phys 46 053508 2005 in the construction of a weyl covariant tensor calculus

reduced complexity soft mimo detection based on causal and noncausal decision feedback we present a reduced complexity soft detection rcsd scheme geared to multiple input multiple output mimo systems with spatial domain multiplexing leading to layered space time or space frequency architecture the proposed algorithm relies on a trellis representation of the mimo signals and a subsequent formulation of constrained depth maximum a posterior map detection in conjunction with soft decision feedback sdf decision feedback is broken into causal and noncausal parts in an effort to maximize the observation window while maintaining a reasonable computational load two variations of rcsd are proposed to utilize the noncausal information in different ways analysis based on mean squared error mse and log likelihood ratio llr associated with symbols in different stages of the trellis is done to develop insight into error propagation in the rcsd algorithm as well as to compare the quality of the soft information obtained by the two rcsd variants error rate simulations are conducted in the context of turbo like iterative demapping and decoding idd the resulting performance and required complexity are compared with those of maximum a posterior map detection soft sphere detection sd as well as the turbo blast processing scheme we observe favorable performance complexity tradeoffs with the proposed soft detection scheme for a number of modulation channel scenarios

quasi maximum likelihood multiuser detection using semi definite relaxation with application to synchronous cdma the maximum likelihood ml multiuser detector is well known to exhibit better bit error rate ber performance than many other multiuser detectors unfortunately ml detection mld is a nondeterministic polynomial time hard np hard problem for which there is no known algorithm that can find the optimal solution with polynomial time complexity in the number of users in this paper a polynomial time approximation method called semi definite sd relaxation is applied to the mld problem with antipodal data transmission sd relaxation is an accurate approximation method for certain np hard problems the sd relaxation ml sdr ml detector is efficient in that its complexity is of the order of k3 5 where k is the number of users we illustrate the potential of the sdr ml detector by showing that some existing detectors such as the decorrelator and the linear minimum mean square error detector can be interpreted as degenerate forms of the sdr ml detector simulation results indicate that the ber performance of the sdr ml detector is better than that of these existing detectors and is close to that of the true ml detector even when the cross correlations between users are strong or the near far effect is significant

iterative tree search detection for mimo wireless systems this paper presents a reduced complexity soft input soft output detection scheme called iterative tree search detection for multiple input multiple output wireless communication systems employing turbo processing at the receiver in this scheme a reduced search space is selected with the aid of the m algorithm and qam signal constellations with block partitionable labels are used in order to make the detection complexity per bit almost independent of the modulation order as well as asymptotically linear in the number of transmit antennas results from computer simulations are presented which demonstrate the capability of the scheme to approach optimal performance at considerably reduced complexity

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

blind ml detection of orthogonal space time block codes efficient high performance implementations orthogonal space time block codes ostbcs have attracted much attention owing to their simple code construction maximal diversity gain and low maximum likelihood ml detection complexity when channel state information csi is available at the receiver this paper addresses the problem of ml ostbc detection with unknown csi focusing on the binary and quaternary psk constellations we show that blind ml ostbc detection can be simplified to a boolean quadratic program bqp from an optimization viewpoint the bqp is still a computationally hard problem and we propose two alternatives for dealing with this inherent complexity first we consider the semidefinite relaxation sdr approach which leads to a suboptimal but accurate blind ml detection algorithm with an affordable worst case computational cost we also consider the sphere decoding approach which leads to an exact blind ml detection algorithm that remains computationally expensive in the worst case but generally incurs a reasonable average computational cost for the two algorithms we study implementation methods that can significantly reduce the computational complexity simulation results indicate that the two blind ml detection algorithms are competitive in that the bit error performance of the two algorithms is almost the same and is noticeably better than that of some other existing blind detectors moreover numerical studies show that the sdr algorithm provides better complexity performance than the sphere decoder in the worst case sense and vice versa in the average sense

on the classification of automorphic lie algebras the problem of reduction of integrable equations can be formulated in a uniform way using the theory of invariants this provides a powerful tool of analysis and it opens the road to new applications of automorphic lie algebras beyond the con text of integrable systems in this paper it is shown that sl2 c based automorphic lie algebras associated to the icosahedral group i the octahedral group o the tetrahedral group t and the dihedral group dn are isomorphic the proof is based on techniques from classical invariant theory and makes use of clebsch gordan decomposition and transvectants molienfunctionsandthetrace form thisresultprovidesacompleteclas sification of sl2 c based automorphic lie algebras associated to finite groups when the group representations are chosen to be the same and it is a crucial step towards the complete classification of automorphic lie algebras

a lattice based approach to option and bond valuation under mean reverting regime switching diffusion processes abstract nowadays the pricing of financial instruments under continuous time markov switching models have received a widespread attention from researchers and practitioners in the finance industry lattice based approaches are amongst the most widely used approaches to solve the pricing problem in this context recently yuen and yang 2010 have proposed a simple and fast recombining trinomial tree method to handle the case of regime switching geometric brownian motion processes in this paper we generalize their approach to the regime switching exponential mean reverting case with state dependent switching rates and derive the necessary conditions for the positivity of conditional branching probabilities we employ the hull and white s tree building procedure to limit tree growth away from the long run mean of the process we use the proposed lattice framework to price contingent claims of european american and barrier type and demonstrate its applicability in pricing default free zero coupon bonds in the proposed tree structure the number of nodes is substantially decreased and the computational cost is effectively reduced compared to the usual approaches extensive numerical experiments illustrate the efficiency and flexibility of the proposed scheme

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

d 2 n 2 superconformally covariant operators and super w algebras we construct and classify superconformally covariant differential operators defined on n 2 super riemann surfaces by contrast to the n 1 theory these operators give rise to partial rather than ordinary differential equations which leads to novel features for their matrix representation the latter is applied to the derivation of n 2 super w algebras in terms of n 2 superfields

moving mesh methods for pricing asian options with regime switching in this paper we study moving mesh implicit finite difference methods for pricing asian options with regime switching the price of asian options with regime switching follows a system of partial differential equations pdes with moving boundaries based on quadratic interpolation between two consecutive levels of computational solutions the moving mesh finite difference methods are constructed to solve the resulted system of pdes with moving boundaries the moving mesh finite difference schemes studied in this paper include implicit euler schemes rannacher schemes and crank nicolson schemes the convergence rates for these schemes are obtained numerical examples are provided to confirm the theoretical results

singular invariant trilinear forms and covariant bi differential operators under the conformal group abstract the residues of the meromorphic family of conformally invariant trilinear forms on the sphere constructed in clerc and orsted in press 2 are computed their expression involves conformally covariant differential and bidifferential operators for the latter new formulae are obtained

reduced complexity soft output mimo sphere detectors part ii architectural optimizations in part i we presented algorithmic optimizations for a soft output so tree search mimo detector targeted at reducing the node count complexity for a given error rate performance we present in this part the architecture for a hardware efficient pipelined detector that incorporates all these optimizations a detailed gate complexity analysis of the architecture is conducted including arithmetic optimizations to minimize the use of multipliers for distance computations by exploiting the lattice structure as well as efficient pointer logic for implementing child enumeration internal node pruning and node skipping steps for multitone ofdm symbol detection using multiple tree search detectors we propose an efficient scheduling scheme that exploits the slack in node count from tone to tone detection by ordering the tones according to increasing order of their channel matrix orthogonality defect the detector maximizes the slack of early terminating detectors and forwards it to ill conditioned tones that require more detection time case studies and simulation experiments were conducted based on a 4 layer 64 qam mimo system for lte simulations and vlsi synthesis results demonstrate that the proposed optimizations require a chip area of only 85 kge to implement a 64 qam so mimo detector for lte capable of attaining almost ml performance with an snr loss of only 0 85 db

convergence rate of regime switching trees considering a general class of regime switching geometric random walks and a broad class of piecewise twice differentiable payoff functions we show that convergence of option prices occurs at a speed of order o n where 1 2 when the payoff is discontinuous and 1 otherwise

soft quasi maximum likelihood detection for multiple antenna wireless channels the paper addresses soft maximum likelihood ml detection for multiple antenna wireless communication channels we propose a soft quasi ml detector that maximizes the log likelihood function by deploying a semi definite relaxation sdr given perfect channel state information at the receiver the quasi ml sdr detector closely approximates the performance of the optimal ml detector in both coded and uncoded multiple input multiple output mimo channels with quadrature phase shift keying qpsk modulation and frequency flat rayleigh fading the complexity of the quasi ml sdr detector is much less than that of the optimal ml detector thus offering more favorable performance complexity characteristics in contrast to the existing sphere decoder the new quasi ml detector enjoys guaranteed polynomial worst case complexity the two detectors exhibit quite comparable performance in a variety of ergodic qpsk mimo channels but the complexity of the quasi ml detector scales better with increasing number of transmit and receive antennas especially in the region of low signal to noise ratio snr

classical w algebras we reconsider the relation between classicalw algebras and deformations of differential operators emphasizing the consistency with diffeomorphisms generators of thew algebra that arek differentials are constructed by a systematic procedure the method extends following drinfeld and sokolov tow algebras based on arbitrary simple lie algebras

performance assessment of mimo bicm demodulators based on mutual information we provide a comprehensive performance comparison of soft output and hard output demodulators in the context of non iterative multiple input multiple output bit interleaved coded modulation mimo bicm coded bit error rate ber widely used in literature for demodulator comparison has the drawback of depending strongly on the error correcting code being used this motivates us to propose the mutual information of the equivalent modulation channel comprising modulator wireless channel and demodulator as a code independent performance measure we present extensive numerical results for spatially independent identically distributed i i d ergodic and quasi static fading channels under perfect and imperfect channel state information these results reveal that the performance ranking of mimo demodulators is rate dependent and provide new insights regarding mimo bicm system design i e the choice of antenna configuration symbol constellation and demodulator for a given target rate

the lie theory of the rankin cohen brackets and allied bi differential operators abstract the lie theoretic nature of the rankin cohen brackets is here uncovered these bilinear operations which among other purposes were devised to produce a holomorphic automorphic form from any pair of such forms are instances of sl 2 r equivariant holomorphic bi differential operators on the upper half plane all of the latter are here characterized and explicitly obtained by establishing their one to one correspondence with singular vectors in the tensor product of two sl 2 c verma modules the rankin cohen brackets arise in the generic situation where the linear span of the singular vectors of a given weight is one dimensional the picture is completed by the special brackets which appear for the finite number of pairs of initial lowest weights for which the above space is two dimensional explicit formulae for basis vectors in both situations are obtained and universal lie algebraic objects subsuming all of them are exhibited a few applications of these results and lie theoretic approach are then considered first a generalization of the latter yields rankin cohen type brackets for hilbert modular forms then some rankin cohen brackets are shown to intertwine the tensor product of two holomorphic discrete series representations of sl 2 r with another such representation occurring in the tensor product decomposition finally the sought for precise relationship between the rankin cohen brackets and gordan s transvection processes of the nineteenth century invariant theory is unveiled

building recombining trinomial trees for time homogeneous diffusion processes abstract time homogeneous diffusion processes are widely applied in finance and economics to model the values of assets two classic examples can be referred to in black and scholes 1973 and cox et al 1985 the applications include investment decisions and pricing derivatives due to mathematical tractability approximation methods such as the monte carlo simulation and the lattice approximation are required in the applications in this paper we present a simple method to construct a recombining trinomial tree to approximate a time homogeneous diffusion process in distribution as an important application of lattice approximation is pricing derivatives we also offer several numerical examples of pricing derivatives to examine our method of constructing recombining trinomial trees

conformal field theories via hamiltonian reduction constraining thesl 3 wzw model we construct a reduced theory which is invariant with respect to the new chiral algebraw 3 2 this symmetry is generated by the stress energy tensor two bosonic currents with spins 3 2 and theu 1 current we conjecture a kac formula that describes the highly reducible representation for this algebra we also discuss the quantum hamiltonian reduction for the general type of constraints that leads to the new extended conformal algebras

function spaces and reproducing kernels on bounded symmetric domains there are several natural hilbert spaces of holomorphic functions on a bounded symmetric domain such are the bergman type spaces on which the holomorphic discrete series operates and the hardy type spaces which are related to the analytic continuation of the holomorphic discrete series also closely related is the bergmann space of entire functions on the ambient which arises as the closure of the polynomials with respect to a natural inner product the space of holomorphic polynomials decomposes into irreducible subspaces under the action of the isotropy group k of the domain the main facts about this decomposition were proved by schmid 21 for another proof see 22 each irreducible subspace contains a unique normalized l invariant spherical polynomial where l is the isotropy group of the shilov boundary in k our first main result is the explicit computation of the norms of the spherical polynomials with respect to each of the hilbert spaces considered for the domains of classical type they were considered by hua 9 and for some of the hilbert spaces this was done before by upmeier 24 using different methods for certain others there are partial results in 22 we are able to do this in a fairly simple unified way by making strong use of gindikin s generalized gamma function s next we obtain a description of the reproducing kernels of the k irreducible subspaces in each of our hilbert spaces and an expansion in terms of these for

knapp stein type intertwining operators for symmetric pairs abstract for a symmetric pair g h of reductive groups we construct a family of intertwining operators between spherical principal series representations of g and h that are induced from parabolic subgroups satisfying certain compatibility conditions the operators are given explicitly in terms of their integral kernels and we prove convergence of the integrals for an open set of parameters and meromorphic continuation in particular this establishes lower bounds for multiplicities of intertwining operators we further discuss uniqueness of intertwining operators and for the rank one cases g h su 1 n f s u 1 m f u n m f with f r c h o and for the pair g h gl 4 n r gl 2 n c we show that for a certain choice of maximal parabolic subgroups our operators generically span the space of intertwiners

two dimensional exactly and completely integrable dynamical systems monopoles instantons dual models relativistic strings lund regge model generalized toda lattice etc an investigation of two dimensional exactly and completely integrable dynamical systems associated with the local part of an arbitrary lie algebra mathfrak g whose grading is consistent with an arbitrary integral embedding of 3d subalgebra in mathfrak g has been carried out we have constructed in an explicit form the corresponding systems of nonlinear partial differential equations of the second order and obtained their general solutions in the sense of a goursat problem a method for the construction of a wide class of infinite dimensional lie algebras of finite growth has been proposed

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

a lattice method for option pricing with two underlying assets in the regime switching model abstract in this work we develop an efficient lattice approach for option pricing with two underlying assets whose prices are governed by regime switching models jump amplitudes are specified in a way such that the lattice achieves complete node recombination along each asset variable and grows quadratically as the number of time steps increases jump probabilities are obtained by solving a related quadratic programming problem the weak convergence of the discrete lattice approximations to the continuous time regime switching diffusion processes is established the lattice is employed to price both european and american options written on the maximum and minimum of two assets in different regimes numerical results are provided and compared for the european options with a monte carlo simulation approach

the relation between quantum w algebras and lie algebras by quantizing the generalized drinfeld sokolov reduction scheme for arbitrarysl2 embeddings we show that a large set open image in new window of quantumw algebras can be viewed as brst cohomologies of affine lie algebras the set open image in new window contains many knownw algebras such asw n andw 3 2 our formalism yields a completely algorithmic method for calculating thew algebra generators and their operator product expansions replacing the cumbersome construction ofw algebras as commutants of screening operators by generalizing and quantizing the miura transformation we show that anyw algebra in open image in new window can be embedded into the universal enveloping algebra of a semisimple affine lie algebra which is up to shifts in level isomorphic to a subalgebra of the original affine algebra thereforeany realization of this semisimple affine lie algebra leads to a realization of thew algebra in particular one obtains in this way a general and explicit method for constructing the free field realizations and fock resolusions for all algebras in open image in new window some examples are explicitly worked out

option pricing with regime switching by trinomial tree method we present a fast and simple tree model to price simple and exotic options in markov regime switching model mrsm with multi regime we modify the trinomial tree model of boyle 1986 12 by controlling the risk neutral probability measure in different regime states to ensure that the tree model can accommodate the data of all different regimes at the same time preserving its combining tree structure in mrsm the market might not be complete therefore we provide some ideas and discussions on managing the regime switching risk in support of our results

semidefinite relaxation based multiuser detection for m ary psk multiuser systems because of the powerful symbol error performance of multiuser maximum likelihood ml detection recently there has been much interest in seeking effective ways of approximating multiuser ml detection mld with affordable computational costs it has been illustrated that for the synchronous code division multiple access cdma scenario the so called semidefinite relaxation sdr algorithm can accurately and efficiently approximate multiuser mld this sdr mld algorithm however can only handle binary and quadratic phase shift keying psk symbol constellations in this sequel we propose an extended sdr algorithm for mld with m ary psk mpsk constellations for the synchronous cdma scenario the proposed sdr algorithm provides an attractive polynomial time complexity order of k sup 3 5 where k is the number of users simulation results indicate that the proposed detector provides improved symbol error performance compared with several commonly used multiuser detectors

a semi analytic valuation of american options under a two state regime switching economy abstract in this study we develop a semi analytic method to evaluate american options under a two state regime switching economy the two free boundaries corresponding to the states divide the pricing domain into two regions a common continuation region and a transition region non linear partial differential equation pde systems are derived under the black scholes framework for each region the laplace transform method is used to solve the pde systems equations for determining the optimal exercise prices are obtained analytically and solved numerically in the laplace space a numerical inversion technique is then used to obtain the free boundaries and the option prices in the original time space the results of various examples show that our technique is efficient and accurate

w algebras and superalgebras from constrained wzw models a group theoretical classification we present a classification ofw algebras and superalgebras arising in abelian as well as non abelian toda theories each model obtained from a constrained wzw action is related with ansl 2 subalgebra resp osp 1 2 superalgebra of a simple lie algebra resp superalgebra g however the determination of anu 1 y factor commuting withsl 2 resp osp 1 2 appears when it exists particularly useful to characterize the correspondingw algebra the super conformal spin contents of eachw super algebra is performed the class of all the superconformal algebras i e with conformal spinss 2 is easily obtained as a byproduct of our general results

option pricing under regime switching jump diffusion models we present an explicit formula and a multinomial approach for pricing contingent claims under a regime switching jump diffusion model the explicit formula obtained as an expectation of merton type formulae for jump diffusion processes allows to compute the price of european options in the case of a two regime economy with lognormal jumps while the multinomial approach allows to accommodate an arbitrary number of regimes and a generic jump size distribution and is suitable for pricing american style options the latter algorithm discretizes log returns in each regime independently starting from the highest volatility regime where a recombining multinomial lattice is established in the remaining regimes lattice nodes are the same but branching probabilities are adjusted derivative prices are computed by a backward induction scheme

second order lattice boltzmann methods for pdes of asian option pricing with regime switching this paper establishes lattice boltzmann models with five amending functions for solving system of partial differential equations pdes arising in asian options pricing with regime switching with the chapman enskog multi scale expansion the pdes are recovered correctly from the continuous boltzmann equation and then the lattice boltzmann method lbm is proposed in the lbm the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants in the traditional lbms the lbm has second order convergence rate in space and first order convergence rate in time the stability convergence rates and computational cost of lbms are studied and verified by numerical examples