pricing derivative securities using integrated quasi monte carlo methods with dimension reduction and discontinuity realignment the dimension and the smoothness of the integrands are the two key factors that affect the efficiency of the quasi monte carlo qmc method the first factor implies that the qmc method can have high performance on a problem with low effective dimension even though its nominal dimension can be very large the second factor suggests that the qmc method can be very effective on a problem that is smooth or even on a problem that is discontinuous as long as its discontinuities are parallel to the axes motivated by these findings methods such as the linear transformation lt method of j imai and k s tan j comput finance 10 2006 pp 129 155 and the orthogonal transformation ot method of x wang and k s tan management sci 59 2013 pp 376 389 have been proposed to increase the efficiency of qmc however both of these methods are unsatisfactory in that they only achieve optimality single sidedly in the sense that the lt method enhances qmc by effective dimension reduction while the o

linearly constrained global optimization a general solution algorithm with applications this paper presents an efficient enumerative approach to solve general linearly constrained optimization problems this class of optimization problems includes fractional nonlinear network models quadratic convex and non convex programs the unified approach is accomplished by converting the constrained optimization problem to an unconstrained optimization problem through a parametric representation of its feasible region the proposed solution algorithm consists of three phases in phase 1 it finds all interior critical points in phase 2 the parametric representation of the feasible region is constructed to identify any critical points on the edges and faces of the feasible region this is done by a modified version of an algorithm for finding the v representation of the polyhedron then in phase 3 the global optimal value of the objective function is found by evaluating the objective function at the critical points as well as at the vertices for an illustration of the algorithm and a comparison with the existing methods small size numerical examples are presented

rigorous application of the stochastic functional method to plane wave scattering from a random cylindrical surface the stochastic functional method is applied to plane wave scattering from a random cylindrical surface whereupon the dirichlet boundary condition is rigorously imposed analytical results accurate to second and fourth order in surface roughness are obtained for the coefficients of the wiener hermite expansion of the secondary scattered wave field the validity of approximate solutions is numerically investigated by means of the boundary condition criterion and of the energy consistency criterion the former which is introduced herein states that any approximate solution should be in conformity with the boundary condition whereas the latter pertains to the energy conservation law the numerical investigation indicates that the rigorous application of the stochastic functional method yields more accurate results in terms of both criteria than did previous treatments of the problem under consideration moreover it is suggested that applicability limits should be set through the mean boundary condition criterion instead of the energy consistency criterion the latter may lead to underestimating deficiencies of the approximate solution under test

analysis of intermittence scale invariance and characteristic scales in the behavior of major indices near a crash abstract this work is devoted to the study of the relation between intermittence and scale invariance we find the conditions that a function in which both effects are present must satisfy and we analyze the relation with characteristic scales we present an efficient method that detects characteristic scales in different systems finally we develop a model that predicts the existence of intermittence and characteristic scales in the behavior of a financial index near a crash and we apply the model to the analysis of several financial indices

a complete algorithm for linear fractional programs abstract the linear fractional programming lfp algorithms attempt to optimize a quotient of two linear functions subject to a set of linear constraints the existing lfp algorithms are problem dependent and none is superior to others in all cases these algorithms explicitly require i the denominator of the objective function does not vanish in the feasible region ii the denominator of the objective function is positive iii the feasible region is bounded moreover some of these algorithms fail whenever iv some constraints are redundant we present a simplex type algorithm which is compact and efficiently detects conditions i iii and relaxes assumption iv the proposed algorithm is evolutionary in the sense that it builds up in a systematic manner to solve any lfp type problems numerical examples illustrate the algorithm

superstatistical fluctuations in time series applications to share price dynamics and turbulence we report a general technique to study a given experimental time series with superstatistics crucial for the applicability of the superstatistics concept is the existence of a parameter beta that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration the proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions we test the method thoroughly with surrogate data sets then the applicability of the superstatistical approach is illustrated using real experimental data we study two examples velocity time series measured in turbulent taylor couette flows and time series of log returns of the closing prices of some stock market indices

optimization of functions with rank two variation over a box abstract this paper deals with optimization of functions that depend on large scale data via a linear transformation of rank two an algorithm is presented which under mild assumptions finds the global solution with polynomial time complexity in the worst case provided the critical points of the objective can be controlled with the same effort moreover for important subclasses of objectives including the linear fractional and the quadratic case we arrive at a linear time algorithm for both cases small simulation studies are provided to illustrate the average case runtime behaviour as a possible application sensitivity of cost assessment in communication networks is addressed where the problems may have tens of thousands of variables

on polynomiality of the method of analytic centers for fractional problems we establish polynomial time convergence of the method of analytic centers for the fractional programming problemt min x g tb x a x k whereg n is a closed and bounded convex domain k m is a closed convex cone anda x g n b x g k are regular enough say affine mappings

stochastic differential equations applied to the study of geophysical and financial time series abstract this work is devoted to the study of modeling geophysical and financial time series we propose a stochastic differential equation arising from the superposition of independent ornstein uhlenbeck processes driven by a a b process superposition of independent a b ornstein uhlenbeck processes offers analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior the stochastic differential equation is applied to geophysics and finance by fitting the superposed a b ornstein uhlenbeck model to typical geophysical and financial time series

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

on asian option pricing for nig levy processes in this paper we derive approximations and bounds for the esscher price of european style arithmetic and geometric average options the asset price process is assumed to be of exponential levy type with normal inverse gaussian nig distributed log returns numerical illustrations of the accuracy of these bounds as well as approximations and comparisons of the nig average option prices with the corresponding black scholes prices are given

visibility graph network analysis of gold price time series abstract mapping time series into a visibility graph network the characteristics of the gold price time series and return temporal series and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory the network degree distribution characters which change from power law to exponent law when the series was shuffled from original sequence and the average path length characters which change from l ln n into ln l ln n as the sequence was shuffled demonstrate that price series and return series are both long rang dependent fractal series the relations of hurst exponent to the power law exponent of degree distribution demonstrate that the logarithmic price series is a fractal brownian series and the logarithmic return series is a fractal gaussian series power law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series the power law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network the hierarchy character in light of the correspondence of graph to price fluctuation means that gold price fluctuation is a hierarchy structure which appears to be in agreement with elliot s experiential wave theory on stock price fluctuation and the local rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent short term factors such as short term speculation

viscoelastic behavior of stock indices abstract the scattering diagram of a stock index results in a complex network structure which can be used to analyze the viscoelastic properties of the index the change along x or y direction of the diagram corresponds to purely elastic or spring like movement whereas the diagonal change at an angle of 45 corresponds to purely viscous or dashpot like movement the viscous component pushes the price from its current value to any other value while the elastic component acts like a restoring force four indices namely dji s p 500 nasdaq 100 and nasdaq composite were studied for the period of 2001 2009 nasdaq composite displayed very high elasticity while nasdaq 100 displayed the highest fluidity in the time period considered the fluidity of dji and s p 500 came out to be close to each other and they are almost the same in the second half of the period

a formula on the wiener hermite expansion two mathematical formulas are given in an explicit form one develops a product of two different multiple wiener integrals in a series of wiener hermite expansions the other one develops a product of two random variables each of which is described by a wiener hermite expansions in a series of another wiener hermite expansion

scattering of a scalar wave from a slightly random surface scalar wave scattering from a slightly random surface is analyzed by a probabilistic method we make use of the homogeneity of an infinite random surface that is the shift invariance property of the strictly homogeneous random field by the group theoretic consideration of such a shift invariance property the wave solution proves to be a homogeneous random field multiplied by an exponential function then such a homogeneous random field is approximately solved for a slightly random surface to yield a wave solution involving multiple scattering several statistical properties of the scattering are calculated and shown in the figures the accuracy of the approximate solution is examined in terms of the error of the boundary value equation

normalized truncated levy walks applied to the study of financial indices abstract this work is devoted to the study of the statistical properties of financial indices from developed and emergent markets we performed a new analysis of the behavior of several financial indices by using a normalized truncated levy walk model we conclude that the truncated levy distribution describes perfectly the evolution of the financial indices near a crash for both well developed and emergent markets

bounds for the price of discrete arithmetic asian options in this paper the pricing of european style discrete arithmetic asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds in our approach we use a general technique for deriving upper and lower bounds for stop loss premiums of sums of dependent random variables as explained in kaas et al ins math econom 27 2000 151 168 and additionally the ideas of rogers and shi j appl probab 32 1995 1077 1088 and of nielsen and sandmann j financial quant anal 38 2 2003 449 473 we are able to create a unifying framework for european style discrete arithmetic asian options through these bounds that generalizes several approaches in the literature as well as improves the existing results we obtain analytical and easily computable bounds the aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters investigate the effect of different conditioning variables and compare their efficiency numerically several sets of numerical results are included we also discuss hedging using these bounds moreover our methods are applicable to a wide range of pricing problems involving a sum of dependent random variables

approximate solution of a mixed nonlinear stochastic oscillator in this paper nonlinear oscillators under mixed quadratic and cubic nonlinearities with stochastic inputs are considered different methods are used to obtain second order approximations namely the wiener hermite and perturbation whep technique and the homotopy perturbation method hpm some statistical moments are computed for the different methods using mathematica 5 comparisons are illustrated through figures for different case studies

generalized box muller method for generating q gaussian random deviates the q gaussian distribution is known to be an attractor of certain correlated systems and is the distribution which under appropriate constraints maximizes a generalization of the familiar shannon entropy this generalized entropy or q entropy provides the basis of nonextensive statistical mechanics a theory which is postulated as a natural extension of the standard boltzmann gibbs statistical mechanics and which may explain the ubiquitous appearance of heavy tailed distributions in both natural and man made systems the q gaussian distribution is also used as a numerical tool for example as a visiting distribution in generalized simulated annealing a simple easy to implement numerical method for generating random deviates from a q gaussian distribution based upon a generalization of the well known box miiller method is developed and presented this method is suitable for a larger range of q values infin q 3 than has previously appeared in the literature and can generate deviates from q gaussian distributions of arbitrary width and center matlab code showing a straightforward implementation is also included

on the explicit evaluation of the geometric asian options in stochastic volatility models with jumps in the present paper we provide a semiexplicit valuation formula for geometric asian options with fixed and floating strike under continuous monitoring when the underlying stock price process exhibits both stochastic volatility and jumps more precisely we shall work in the barndorff nielsen and shephard bns model framework we shall provide some numerical illustrations of the results obtained

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

scattering of waves from a random spherical surface mie scattering the stochastic theory developed by the authors for the scattering from a random planar surface is extended to the case of a random spherical surface which is assumed to be a homogeneous random field on the sphere homogeneous with respect to spherical rotations based on the group theoretical analogies between the two the formulation of the theory is closely connected to the representation theory of the rotation group the concept of the stochastic spherical harmonics associated with the rotation group and their several formulas are introduced and discussed at the beginning for the plane wave incident on a random spherical surface the scattered random wave field can be expanded systematically in terms of the stochastic spherical harmonics in much the same way as the nonrandom case and several formulas are derived for the coherent scattering amplitude the coherent and incoherent power flows and the coherent and incoherent scattering cross sections the power flow conservation law is cast into the stochastic version of the optical theorem stating that the total scattering cross section consisting of the coherent and incoherent power flow is equal to the imaginary part of the coherent forward scattering amplitude approximate solutions are obtained for the mie scattering with a slightly random spherical surface where the single scattering approximation is valid due to the absence of a real resonance as shown in the previous work on the two dimensional case some numerical calculations are made for the coherent and incoherent scattering cross sections

path integral approach to closed form option pricing formulas with applications to stochastic volatility and interest rate models we present a path integral method to derive closed form solutions for option prices in a stochastic volatility model the method is explained in detail for the pricing of a plain vanilla option the flexibility of our approach is demonstrated by extending the realm of closed form option price formulas to the case where both the volatility and interest rates are stochastic this flexibility is promising for the treatment of exotic options our analytical formulas are tested with numerical monte carlo simulations

criss cross methods a fresh view on pivot algorithms criss cross methods are pivot algorithms that solve linear programming problems in one phase starting with any basic solution the first finite criss cross method was invented by chang terlaky and wang independently unlike the simplex method that follows a monotonic edge path on the feasible region the trace of a criss cross method is neither monotonic with respect to the objective function nor feasibility preserving the main purpose of this paper is to present mathematical ideas and proof techniques behind finite criss cross pivot methods a recent result on the existence of a short admissible pivot path to an optimal basis is given indicating shortest pivot paths from any basis might be indeed short for criss cross type algorithms the origins and the history of criss cross methods are also touched upon

coupled continuous time random walk approach to the rachev ruschendorf model for financial data abstract in this paper we expand the rachev ruschendorf asset pricing model introducing a coupled continuous time random walk ctrw like form of the random number of price changes such a form results from the concept of the random clustering procedure that resembles the coarse graining methods of statistical physics and on the other hand indicates applicability of the ctrw idea widely used in physics to model anomalous diffusion for describing financial markets in the framework of the proposed model we derive the limiting distributions of log returns and the corresponding pricing formulas for european call option in order to illustrate the obtained theoretical results we present their fitting with several sets of financial data

volatility in the italian stock market an empirical study we study the volatility of the mib30 stock index high frequency data from november 28 1994 through september 15 1995 our aim is to empirically characterize the volatility random walk in the framework of continuous time finance to this end we compute the index volatility by means of the log return standard deviation we choose an hourly time window in order to investigate intraday properties of volatility a periodic component is found for the hourly time window in agreement with previous observations fluctuations are studied by means of detrended fluctuation analysis and we detect long range correlations volatility values are log stable distributed we discuss the implications of these results for stochastic volatility modelling

pricing bounds for discrete arithmetic asian options under levy models abstract analytical bounds for asian options are almost exclusively available in the black scholes framework in this paper we derive bounds for the price of a discretely monitored arithmetic asian option when the underlying asset follows an arbitrary levy process explicit formulas are given for kou s model merton s model the normal inverse gaussian model the cgmy model and the variance gamma model the results are compared with the comonotonic upper bound existing numerical results monte carlo simulations and in the case of the variance gamma model with an existing lower bound the method outlined here provides lower and upper bounds that are quick to evaluate and more accurate than existing bounds

levy walks and enhanced diffusion in milan stock exchange abstract we perform statistical analyses of the general and sectorial historical m i b indices of the milan stock exchange our analyses show that the price indices have statistical properties which are compatible with a levy random walk the time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior by using the theory of enhanced diffusion in levy walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time

closed form approximations for diffusion densities a path integral approach in this paper we investigate the transition probabilities for diffusion processes in a first part we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral for several classical models an exact calculation is possible leading to analytical expressions for the transition probabilities and for the maximum probability paths a second part consists of the derivation of an analytical approximation for the transition probability which is useful in case the path integral is too complex to be calculated the approximation we present is based on a convex combination of a new analytical upper and lower bound for the transition probabilities the fact that the approximation is analytical has some important advantages e g for the investigation of asian options finally we demonstrate the accuracy of the approximation by means of some graphical illustrations

a parametric method for solving the linear fractional programming problem this paper describes an approach for determining the optimal solution of the linear fractional programming problem this approach is based mainly on a parametric analysis of a related linear substitution problem whereas existing algorithms for linear fractional programs concentrate solely on determining the optimal solution the approach described in this paper provides the decision maker with additional insights and valuable information on the underlying decision problem when the usual algorithms are applied this additional information which is gained by the parametric analysis of the substitution problem can be obtained only by further computational effort

wiener analysis of a binary hysteresis system nonlinear transformation of an independent gaussian sequence by a binary hysteresis is studied by wiener s method nonlinear problems in random theory mit cambrige ma 1958 the output sequence of the hysteresis is represented by a series of wiener hermite functionals which are random and orthogonal uncorrelated to each other from the hysteresis equation a set of linear equations for the wiener hermite functionals is derived without approximation the equations directly show that the hysteresis is decomposed into equivalent subsystems consisting of static nonlinear elements multipliers adders and linear filters they are solved by use of random numbers generated in a computer in order to get a sample output sequence approximated by a finite sum of the wiener hermite functionals another set of equations is derived for the mean square values of the wiener hermite functionals in terms of its numerical solutions the convergence property of the wiener hermite functional series is discussed

analytic model for transient anomalous diffusion with highly persistent correlations in recent decades many stochastic processes have been proposed as models for real world time series data with anomalous spreading highly persistent correlations and transient distributional characteristics we introduce the higher order fractional tempered stable motion as the stochastic integral of the tempered stable motion with respect to a generalized higher order moving average kernel which provides an analytic model for stochastic processes possessing these characteristics this stochastic process provides a mathematical model for anomalous diffusion with a transient distribution resembling higher order fractional stable motion on short timescales and higher order fractional brownian motion in the long run the specifics of the crossover dynamics from the levy stable anomalous diffusion to the gaussian anomalous diffusion are controlled by explicit parameter values that correspond to physical attributes of the process it is well suited to modeling anomalous diffusion of any type sub super regular or hyperdiffusion under appropriate parametrizations due to its power law scaling of variance with respect to time it is also a useful model for position velocity acceleration triples due to its convenient path differentiability and integrability properties to highlight the potential physical relevance of this model for real world data we outline its key statistical properties including its covariance structure memory and second order self similarity we also give an easy to implement elementary method for sample path generation which may be used as a basis for simulation and monte carlo studies

a simple method for obtaining weakly efficient points in multiobjective linear fractional programming problems abstract the properties of linear fractional functions facilitate the usage of a well known scalar optimization problem that gives weakly efficient points separately the weak efficiency can be detected with another scalar optimization test based on the same properties the numerical estimation of the nadir vector is considered as a possible application

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

fractional programming applications and algorithms abstract the paper deals with decision problems that give rise to the optimization of ratios subject to constraints these so called fractional programs have been treated in a considerable number of papers it is attempted to survey applications as well as solution methods in linear quadratic and concave convex fractional programming in the first part we give a detailed outline on the major areas of applications of fractional programming following a brief review on some basic theoretical results like duality relations in the second part we then discuss different algorithmic approaches a primal a dual and a parametric solution method is considered here we try to determine for each method the kind of fractional programs that are solved by it suitably

moments for tempered fractional advection diffusion equations this paper develops moment formulas for exponentially tempered fractional advection diffusion equations tfades that transition from anomalous to asymptotic diffusion limits over time exact analytical expressions or series representations for spatial moments up to the fourth order are derived by integral transform or asymptotic expansion approach a fully lagrangian solver cross verified by an implicit eulerian approach is also developed to calculate numerically the complete evolution of moments for the tfades with complex initial and boundary conditions moment analysis identifies the diffusion equation that attracts the tempered anomalous diffusion in the long time limit fitting of moments measured at two end members of alluvial systems checks the applicability of moment analysis in understanding real diffusion

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

on algorithmic equivalence in linear fractional programming this paper compares the effectiveness of three published algorithms for solving the linear fractional programming problem consider the problem maximize f x c x a d x 8 subject to ax o where a e rrxn b e rm c d e r a e r and d x 0 for all feasible x charnes and cooper 1 isbell and marlow 2 and martos in his simple case in 3 and in 4 have each given a technique for solving such a linear fractional programming problem when the constraint set is bounded wagner and yuan 5 show that for this problem the methods of charnes and cooper 1 and martos 4 are algorithmically equivalent in the sense that the two algorithms select the same nonbasic variables to enter the next trial solution and remove the same basic variable from the current solution here we compare the technique of isbell and marlow 2 which involves the solution of a sequence of linear programs to those of charnes cooper and martos we point out that they are not equivalent in that the isbell marlow method only checks for optimality of the fractional program at points that are optimal solutions of intermediary linear programs whereas charnes cooper and martos check for optimality of the fractional program at each step of the simplex method indeed the isbell marlow method unlike the other two may actually reach the optimal vertex and not recognize that the point is optimal it will then proceed or try to proceed to another nonoptimal vertex if the feasible set is bounded the procedure will eventually return to the optimal point if the feasible set is unbounded the isbell marlow method may fail 2 whereas the charnes cooper and received june 14 1979 revised november 7 1980 1980 mathematics subject classification primary 90c05 90c30 charnes cooper 1 and martos 4 suggest that if the feasible set is unbounded the problem can be regularized as described in 4 this involves adding the constraint xi x2 xn m for sufficiently large m 2 we emphasize that solution procedures given by their authors for problems with bounded constraint sets are here being used without regularization on problems with unbounded constraint sets martos 4 himself gives an example in which his method fails in such a case our point here is that the martos method may succeed where the isbell marlow method does not and that the charnes cooper will surprisingly always obtain a finite optimal if it exists even though it is necessary in a sense to proceed through an infinite point before reaching the finite optimal solution 1981 american mathematical society 0025 5718 81 0000 01 14 01 75

long correlations and truncated levy walks applied to the study latin american market indices abstract this work is devoted to the study of long correlations and other statistical properties of latin american market indices we concluded that the behavior of the return is compatible with a slow convergence to a gaussian distribution we also detected long range correlations in the absolute value of the return analyzing the effects of working with short data series this fact has relevant consequences in the volatility dynamics

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

general optimized lower and upper bounds for discrete and continuous arithmetic asian options we propose an accurate method for pricing arithmetic asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation in particular we derive analytical expressions for the lower bound in the fourier domain this is then recovered by a single univariate inversion and sharpened using an optimization technique in addition we derive an upper bound to the error from the lower bound price approximation our proposed method can be applied to computing the prices and price sensitivities of asian options with fixed or floating strike price discrete or continuous averaging under a wide range of stochastic dynamic models including exponential levy models stochastic volatility models and the constant elasticity of variance diffusion our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases

the finite criss cross method for hyperbolic programming in this paper the finite criss cross method is generalized to solve hyperbolic fractional linear programming problems just as in the case of linear or quadratic programming the criss cross method can be initialized with any not necessarily feasible basic solution it is known that if the feasible region of the problem is unbounded then some of the known algorithms fail to solve the problem our criss cross algorithm does not have such drawback finiteness of the procedure is proved under the usual mild assumptions some small numerical examples illustrate the main features of the algorithm and show that our method generates different iterates than other earlier published methods

the linear complimentarity problem sufficient matrices and the criss cross method specially structured linear complementarity problems lcps and their solution by the criss cross method are examined the criss cross method is known to be finite for lcps with positive semidefinite bisymmetric matrices and with p matrices it is also a simple finite algorithm for oriented matroid programming problems recently cottle pang and venkateswaran identified the class of column row sufficient matrices they showed that sufficient matrices are a common generalization of p and psd matrices cottle also showed that the principal pivoting method with a clever modification can be applied to row sufficient lcps in this paper the finiteness of the criss cross method for sufficient lcps is proved further it is shown that a matrix is sufficient if and only if the criss cross method processes all the lcps defined by this matrix and all the lcps defined by the transpose of this matrix and any parameter vector

a combined phase i phase ii projective algorithm for linear programming we devise a projective algorithm which explicitly considers the constraint that an artificial variable be zero at the solution inclusion of such a constraint allows the algorithm to be applied to a possibly infeasible standard form linear program without the addition of any bigm terms or conversion to a primal dual problem

default prediction with the merton type structural model based on the nig levy process merton s model merton 1974 has long been a standard for estimating company s probability of default pd for listed companies the major advantage of merton s model is the use of current market prices to determine the probability of default the logic behind the model is simple the market prices best reflect all the relevant information being forward looking estimates of company s prospect and should be and are superior to the balance sheet disclosures which at best are ex post realisations of company s performance it is thus a pity that the benefits strengths of merton s model are hindered by a significant shortcoming of the model namely the assumption of normally distributed returns as numerous authors point out barndorff nielsen 1997 5 6 prause 1999 eberlein 2001 brambilla et al 2015 stock returns are not normally distributed which significantly limits the use of model in practice moreover the estimates of pds can be biased downwards exposing the banks to the possibility of undercapitalisation and systematic shocks it is the purpose of this paper to remedy this situation firstly we extend the merton model by allowing for normal inverse gaussian nig distributed returns as several authors point out using the examples of options schoutens 2009 nig in most cases provides a robust statistical platform for estimating stock returns we further extend our approach by constructing a robust em algorithm for estimating pds within the merton nig framework we also test the reliability of the nig improved merton model against classical merton s model for estimating pds applying our results to ljubljana stock exchange we find that the pd estimates using classical merton s model are biased whereas the estimates from nig merton s model are robust

an interior point method for generalized linear fractional programming we develop an interior point polynomial time algorithm for a generalized linear fractional problem the latter problem can be regarded as a nonpolyhedral extension of the usual linear fractional programming typical example which is of interest for control theory is the minimization of the generalized eigenvalue of a pair of symmetric matrices linearly depending on the decision variables

a computationally stable solution algorithm for linear programs an active area of research for linear programming is to construct initial simplex tableau that is close to the optimal solution and to improve its pivoting selection strategies efficiently in this paper we present a new approach to the problem of initialization and pivoting rules the algorithm is free from any artificial variables and artificial constraints known as the big m methods by supplying the simplex method without using any large numbers therefore the result is computationally stable and provides a better initial basis that reduces the number of pivoting iterations efficiency a three phase simplex type solution algorithm is developed for solving general linear programs in phase 1 greater than constraints are relaxed and the problem is solved starting at the origin if it is unbounded then the objective function is modified in order to have a bound feasible solution then in phase 2 the greater than constraints are introduced in a dual simplex framework following this in the case the original objective function was modified phase 3 restores optimality for the original objective function the algorithm is numerically stable and works with the original decision variables our initial experimental study indicates that the proposed algorithm is more efficient than both the primal and the dual simplex in terms of the number of iterations

empirical fractal geometry analysis of some speculative financial bubbles abstract empirical evidence of a multifractal signature during increasing of a financial bubble leading to a crash is presented the april 2000 crash in the nasdaq composite index and a time series from the discrete chakrabarti stinchcombe model for earthquakes are analyzed using a geometric approach and some common patterns are identified these patterns can be related the geometry of the rising period of a financial bubbles with the non concave entropy problem

the role of pivoting in proving some fundamental theorems of linear algebra abstract we give a constructive proof for some classical theorems of linear algebra steinitz rank of matrices rouche kronecker capelli farkas wey minkowski the construction is based on pivoting and its most important part is the pivot selection rule which is based on bland s least index resolution

exponentially damped levy flights abstract since real processes seem to departure from standard levy distributions modifications to the latter have been suggested in literature these include abruptly truncated phys rev lett 73 1994 2946 smoothly truncated phys rev e 52 1995 1197 phys lett a 266 2000 282 and gradually truncated levy flights physica a 268 1999 231 physica a 275 2000 531 we put forward what we call an exponentially damped levy flight which encompasses the previous cases in the presence of increasing and positive feedbacks our distribution is assumed to deviate from the levy in both a smooth and gradual fashion we estimate the truncation parameters by nonlinear least squares to optimally fit the distribution tails that is a novel approach for estimating parameters and of the levy the method is illustrated with daily data on exchange rates for 15 countries against the us dollar our results show that the exponentially damped levy flight fits the data well when increasing and positive deviations are present

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess