multivariate jacobi process with application to smooth transitions abstract we introduce the multivariate jacobi process as a representation for the dynamics of a stochastic discrete probability distribution its domain of application is dynamic analysis of switching regimes in asset return volatility business cycle and corporate credit ratings the paper shows how the multivariate jacobi process is derived from the multivariate cox ingersoll ross cir model by time deformation and presents the main distributional properties for illustration selected continuous time models of prices and returns on financial assets are extended to smooth transitions processes featuring regimes of different volatilities and persistence in this framework the effects of transitions between the regimes on derivative prices and long memory are examined

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

exact number of solutions of stationary reaction diffusion equations we study both existence and the exact number of positive solutions of the problem p l l u p 2u f u 0in 0 1 u 0 u 1 0 where l is a positive parameter p 1 the nonlinearity f is positive in 0 1 and f 0 f 1 0 assuming that f satisfies the condition lim s 1 f s 1 s email protected 0 where email protected 0 p 1 we study its behavior near zero and we obtain existence and exactness results for positive solutions we prove the results using the shooting method we show that there always exist solutions with a flat core for l sufficiently small as an application we prove the existence of a non negative solution for a class of singular quasilinear elliptic problems in a bounded domain in r n having a flat core in a ball

stationary profiles of degenerate problems with inhomogeneous saturation values abstract this work is concerned with the profiles of solutions for stationary problems between the degenerate diffusion of the p laplacian and a reaction with an inhomogeneous saturation value it is shown that if a parameter for the diffusion is sufficiently small then the solution attains the saturation value of the reaction in each region where the saturation value is constant the associated evolutional problem is also mentioned

finite mixture distributions sequential likelihood and the em algorithm a popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution a barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly using mixture distributions destroys any additive separability of the log likelihood function we show however that an extension of the em algorithm reintroduces additive separability thus allowing one to estimate parameters sequentially during each maximization step in establishing this result we develop a broad class of estimators for mixture models returning to the likelihood problem we show that relative to full information maximum likelihood our sequential estimator can generate large computational savings with little loss of efficiency

linear sparse differential resultant formulas abstract let p be a system of n linear nonhomogeneous ordinary differential polynomials in a set u of n 1 differential indeterminates differential resultant formulas are presented to eliminate the differential indeterminates in u from p these formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in p or in a linear perturbation p e of p in particular the formula fres p is the determinant of a matrix m p having no zero columns if the system p is super essential as an application if the system p is sparse generic such formulas can be used to compute the differential resultant res p introduced by li et al 2011 19

bayesian inference and state number determination for hidden markov models an application to the information content of the yield curve about inflation this paper is concerned with bayesian inference in hidden markov models focusing on switching regression models we propose a new methodology that delivers a joint estimation of the parameters and the number of regimes that have actually appeared in the studied sample the only prior information that is required on the latter quantity is an upper bound we implement a particle filter algorithm to compute the corresponding estimates applying this methodology to the information content of the yield curve regarding future inflation in four oecd countries we show that the predictive content for given country and combination of maturities is subject to regime switching

maximum likelihood estimation for multivariate observations of markov sources parameter estimation for multivariate functions of markov chains a class of versatile statistical models for vector random processes is discussed the model regards an ordered sequence of vectors as noisy multivariate observations of a markov chain mixture distributions are a special case the foundations of the theory presented here were established by baum petrie soules and weiss a powerful representation theorem by fan is employed to generalize the analysis of baum em et al to a larger class of distributions

classification of bifurcation diagrams of a p laplacian dirichlet problem with examples abstract we study bifurcation diagrams of positive solutions of the p laplacian dirichlet problem p u x f u x 0 1 x 1 u 1 u 1 0 where p y y p 2 y p u is the one dimensional p laplacian and p 1 and 0 are two bifurcation parameters assume that f u g u h u where g h c 0 c 2 0 satisfy hypotheses h1 h5 presented herein for different values p with 1 p 2 and with p 2 we give a classification of totally six different bifurcation diagrams we prove that on the u plane each possible bifurcation diagram consists of exactly one curve with exactly one turning point where the curve turns to the right hence we are able to determine the exact multiplicity of positive solutions in addition for 1 p 2 and for p 2 we give interesting examples f u k u p 1 u q u r satisfying r q p 1 and k 0 and show complete evolution of bifurcation diagrams as evolution parameter k varies from 0 to

on the shape of the nonnegative solutions to a singularly perturbed quasilinear dirichlet problem abstract we study the shape of the nontrivial nonnegative solutions for a singularly perturbed quasilinear dirichlet problem with non lipschitz nonlinearity we find that there exists at least one nontrivial nonnegative solution of the problem which consists of some bubbles the profile of each bubble is discussed

exact multiplicity for some quasilinear elliptic dirichlet problems where the non linearity changes sign abstract the exact multiplicity of positive solutions is obtained for a class of quasilinear elliptic dirichlet problems where the non linearity changes sign meanwhile the uniqueness of positive ground state on r n is also obtained

turbo segmentation of textured images we consider the problem of semi supervised segmentation of textured images existing model based approaches model the intensity field of textured images as a gauss markov random field to take into account the local spatial dependencies between the pixels classical bayesian segmentation consists of also modeling the label field as a markov random field to ensure that neighboring pixels correspond to the same texture class with high probability well known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion but these techniques are usually computationally intensive because they require a large number of iterations to converge in this paper we propose a new bayesian framework by modeling two dimensional textured images as the concatenation of two one dimensional hidden markov autoregressive models for the lines and the columns respectively a segmentation algorithm which is similar to turbo decoding in the context of error correcting codes is obtained based on a factor graph approach the proposed method estimates the unknown parameters using the expectation maximization algorithm

continuity properties on p for p laplacian parabolic problems abstract in this work we obtain some continuity properties on the parameter p at p 2 for the takeuchi yamada problem which is a degenerate p laplacian version of the chafee infante problem we prove the continuity of the flows and the equilibrium sets and the upper semicontinuity of the global attractors

coincidence sets in quasilinear elliptic problems of monostable type abstract this paper concerns the formation of a coincidence set for the positive solution of the boundary value problem e p u u q 1 f a x u in with u 0 on where e is a positive parameter p u div u p 2 u 1 q p f s s 1 s s 0 for some 0 and a x is a positive smooth function satisfying p a 0 in with inf a 0 it is proved in this paper that if 0 1 the coincidence set o e x u e x a x has a positive measure for small e and converges to with order o e 1 p as e 0 moreover it is also shown that if 1 then o e is empty for any e 0 the proofs rely on comparison theorems and the energy method for obtaining local comparison functions

analysis of time series subject to changes in regime abstract this paper introduces an em algorithm for obtaining maximum likelihood estimates of parameters for processes subject to discrete shifts in autoregressive parameters with the shifts themselves modeled as the outcome of a discrete valued markov process the simplicity of the em algorithm permits potential application of the approach to large vector systems

recognition of degraded characters using dynamic bayesian networks in this paper we investigate the application of dynamic bayesian networks dbns to the recognition of degraded characters dbns are an extension of one dimensional hidden markov models hmms which can handle several observation and state sequences in our study characters are represented by the coupling of two hmm architectures into a single dbn model the interacting hmms are a vertical hmm and a horizontal hmm whose observable outputs are the image columns and image rows respectively various couplings are proposed where interactions are achieved through the causal influence between state variables we compare non coupled and coupled models on two tasks the recognition of artificially degraded handwritten digits and the recognition of real degraded old printed characters our models show that coupled architectures perform more accurately on degraded characters than basic hmms the linear combination of independent hmm scores as well as discriminative methods such as support vector machines svms

a monte carlo based approach for pricing credit default swaps with regime switching abstract this paper considers the valuation of a cds credit default swap contract to find out a more accurate cds price we work on an extended merton s model by assuming that the price of the reference asset follows a regime switching black scholes model and moreover the reference asset can default at any time before the expiry time a general pricing formula for the cds containing the unknown no default probability is derived first it is then subsequently shown that the no default probability is equivalent to the price of a down and out binary option written on the same reference asset by simulating the markov chain with the monte carlo technique we obtain an approximation formula for the down and out binary option with the availability of which the calculation of the cds price becomes straightforward finally some numerical experiments are conducted to examine the accuracy of the approximation approach as well as the impacts of the introduction of the regime switching mechanics on the cds price

generalized jacobian elliptic functions and their application to bifurcation problems associated with p laplacian abstract the jacobian elliptic functions are generalized and applied to bifurcation problems associated with p laplacian the values of bifurcation parameter and the corresponding solutions are represented in terms of common parameters and a complete description of the bifurcation diagram and a closed form representation of the corresponding solutions are obtained as a by product of the representation it turns out that a kind of solution is also a solution of an eigenvalue problem of p 2 laplacian

stationarity of multivariate markov switching arma models in this article we consider multivariate arma models subject to markov switching in these models the parameters are allowed to depend on the state of an unobserved markov chain a natural idea when estimating these models is to impose local stationarity conditions i e stationarity within each regime in this article we show that the local stationarity of the observed process is neither sufficient nor necessary to obtain the global stationarity we derive stationarity conditions and we compute the autocovariance function of this nonlinear process interestingly it turns out that the autocovariance structure coincides with that of a standard arma some examples are proposed to illustrate the stationarity conditions using monte carlo simulations we investigate the consequences of accounting for the stationarity conditions in statistical inference

value at risk via mixture distributions reconsidered value at risk var has evolved as one of the most prominent measures of downside risk in financial markets zhang and cheng m h zhang q s cheng an approach to var for capital markets with gaussian mixture applied mathematics and computation 168 2005 1079 1085 proposed an approach to var for daily returns based on gaussian mixtures which have become rather popular in empirical economics and finance since the seminal paper of hamilton j d hamilton a new approach to the economic analysis of nonstationary time series and the business cycle econometrica 57 2 1989 357 384 however they do not conduct tests to assess the accuracy of the mixture implied var measures recently guidolin and timmermann m guidolin a timmermann term structure of risk under alternative econometric specifications journal of econometrics 131 2006 285 308 showed that markov mixture models do well in measuring var at a monthly frequency but the results may not hold for daily returns due to their more pronounced non gaussian features this paper provides an extensive application of various markov mixture models to var for daily returns of major european stock markets including out of sample backtesting to accommodate the properties of daily returns we consider both gaussian and student s t mixtures and we compare the performance of both uni and multivariate models under different parameter updating schemes we find that a univariate mixture of two student s t distributions performs best overall however by the example of the recent turmoil in financial markets we also highlight a weak point of the approach

specification testing in markov switching time series models this paper develops a series of specification tests of markov switching time series models tests for omitted autocorrelation omitted arch misspecification of the markovian dynamics and omitted explanatory variables are proposed all of the tests can be constructed as a natural byproduct of the routine used to calculate the smoothed probability that a given observation came from a particular regime and do not require estimation of additional parameters the paper performs monte carlo analysis of the tests and briefly illustrates their use with an empirical application

serial correlation in latent discrete variable models abstract we consider the problems of estimation and testing in models with serially correlated discrete latent variables a particular case of this is the time series regression model in which a discrete explanatory variable is measured with error test statistics are derived for detecting serial correlation in such a model we then show that the likelihood function can be evaluated by a recurrence relation and thus maximum likelihood estimation is computationally feasible an illustrative example of these methods is given followed by a brief discussion of their applicability to a markov model of switching regressions

a series form solution for pricing variance and volatility swaps with stochastic volatility and stochastic interest rate abstract in this paper we present analytical pricing formulae for variance and volatility swaps when both of the volatility and interest rate are assumed to be stochastic and follow a cir cox ingersoll ross process forming a heston cir hybrid model the solutions are written in a series form with a theoretical proof of their convergence ensuring the accuracy of the determined swap prices the application of the formulae in practice is also demonstrated through the designed numerical experiments

multiplicity result for a degenerate elliptic equation with logistic reaction abstract a degenerate elliptic equation pu uq 1 1 ur 0 with zero dirichlet boundary condition where is a positive parameter 2 0 is studied it has been known that there exists a positive number such that if then the problem has no positive solution if then there exists a maximal solution and for sufficiently small

infinitely many nodal solutions for generalized logistic equations without odd symmetry on reaction abstract we consider nonlinear parametric logistic type equations driven by a nonlinear nonhomogeneous differential operator the reaction term is a caratheodory function which is not assumed to be odd the subdiffusive equidiffusive and superdiffusive cases are all treated we prove the existence of infinitely many nodal solutions we also prove a bifurcation type result describing the dependence of the set of constant sign solutions on the parameter in the superdiffusive case our approach uses variational methods together with upper lower solutions and truncation techniques and flow invariance arguments

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

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

a new approximate likelihood estimator for arma filtered hidden markov models hidden markov models hmms are successfully applied in various fields of time series analysis colored noise e g due to filtering violates basic assumptions of the model although it is well known how to consider autoregressive ar filtering there is no algorithm to take into account moving average ma filtering in parameter estimation exactly we present an approximate likelihood estimator for ma filtered hmm that is generalized to deal with an autoregressive moving average arma filtered hmm the approximation order of the likelihood calculation can be chosen therefore we obtain a sequence of estimators for the hmm parameters as well as for the filter coefficients the recursion equations for an efficient algorithm are derived from exact expressions for the forward iterations by simulations we show that the derived estimators are unbiased in filter situations where standard hmm s are not able to recover the true dynamics special implementation strategies together with small approximations yield further acceleration of the algorithm

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

on p laplacian differential inclusions global existence compactness properties and asymptotic behavior abstract in this work we consider coupled systems of p laplacian differential inclusions we obtain the global existence of solutions and good compactness properties in such way that the set of all possible solutions compose a generalized semiflow which has a global attractor for each pair of positive diffusion coefficients we also prove that the attractors are upper semicontinuous on positive finite diffusion parameters

estimation of markov regime switching regression models with endogenous switching abstract following hamilton 1989 a new approach to the economic analysis of nonstationary time series and the business cycle econometrica 57 357 384 estimation of markov regime switching regressions typically relies on the assumption that the latent state variable controlling regime change is exogenous we relax this assumption and develop a parsimonious model of endogenous markov regime switching inference via maximum likelihood estimation is possible with relatively minor modifications to existing recursive filters the model nests the exogenous switching model yielding straightforward tests for endogeneity in monte carlo experiments maximum likelihood estimates of the endogenous switching model parameters were quite accurate even in the presence of certain model misspecifications as an application we extend the volatility feedback model of equity returns given in turner et al 1989 a markov model of heteroskedasticity risk and learning in the stock market journal of financial economics 25 3 22 to allow for endogenous switching

multivariate contemporaneous threshold autoregressive models this paper proposes a contemporaneous threshold multivariate smooth transition autoregressive c mstar model in which the regime weights depend on the ex ante probabilities that latent regime specific variables exceed certain threshold values a key feature of the model is that the transition function depends on all the parameters of the model as well as on the data since the mixing weights are also a function of the regime specific noise covariance matrix the model can account for contemporaneous regime specific co movements of the variables the stability and distributional properties of the proposed model are discussed as well as issues of estimation testing and forecasting the practical usefulness of the c mstar model is illustrated by examining the relationship between us stock prices and interest rates

pricing variance and volatility swaps with stochastic volatility stochastic interest rate and regime switching abstract in this paper we propose a two factor heston cir hybrid model for the pricing of variance and volatility swaps by introducing the second regime switching factor into the heston cir hybrid model while this model is closer to reality taking advantages of the heston stochastic volatility cir stochastic interest rate and regime switching it has a more complicated structure and thus leads to extra difficulty in finding analytical solutions albeit difficult we have still managed to present analytical pricing formulae for variance and volatility swaps based on the derived forward characteristic function in a series form the series solutions are accompanied by a radius of convergence to ensure its safe application and their fast convergence demonstrated through numerical experiments facilitates the implementation in practice

structures and evolution of bifurcation diagrams for a one dimensional diffusive generalized logistic problem with constant yield harvesting abstract we study the one dimensional diffusive generalized logistic problem with constant yield harvesting u x g u 0 1 x 1 u 1 u 1 0 where 0 we assume that nonlinearity g satisfies g 0 g 1 0 g u 0 on 0 1 and g either is concave on 0 1 or is concave convex on 0 1 and satisfies a certain condition we prove that for any fixed 0 on the u plane the bifurcation diagram consists of a shaped curve and then we study the structures and evolution of bifurcation diagrams for varying 0 we also prove that for any fixed 2 4 g 0 on the u plane the bifurcation diagram consists of a reversed shaped curve and then we study the structures and evolution of bifurcation diagrams for varying 2 4 g 0

nonlinearities and regimes in conditional correlations with different dynamics abstract new parameterizations of the dynamic conditional correlation dcc model and of the regime switching dynamic correlation rsdc model are introduced such that these models provide a specific dynamics for each correlation they imply a nonlinear autoregressive form of dependence on lagged correlations and are based on properties of the hadamard exponential matrix the new models are applied to a data set of twenty stock market indices and a data set of the thirty dow jones components comparing them to the classical dcc and rsdc models the empirical results show that the new models improve their classical versions in terms of several criteria

markov switching model selection using kullback leibler divergence abstract in markov switching regression models we use kullback leibler kl divergence between the true and candidate models to select the number of states and variables simultaneously specifically we derive a new information criterion markov switching criterion msc which is an estimate of kl divergence msc imposes an appropriate penalty to mitigate the over retention of states in the markov chain and it performs well in monte carlo studies with single and multiple states small and large samples and low and high noise we illustrate the usefulness of msc via applications to the u s business cycle and to media advertising

regime switching dynamic correlations for asymmetric and fat tailed conditional returns abstract a non gaussian multivariate regime switching dynamic correlation model for financial asset returns is proposed it incorporates the multivariate generalized hyperbolic law for the conditional distribution of returns all model parameters are estimated consistently using a new two stage expectation maximization algorithm that also allows for incorporation of shrinkage estimation via quasi bayesian priors it is shown that use of markov switching correlation dynamics not only leads to highly accurate risk forecasts but also potentially reduces the regulatory capital requirements during periods of distress in terms of portfolio performance the new regime switching model delivers consistently higher sharpe ratios and smaller losses than the equally weighted portfolio and all competing models finally the regime forecasts are employed in a new dynamic risk control strategy that avoids most losses during the financial crisis and vastly improves risk adjusted returns

binomial markov switching multifractal model with skewed t innovations and applications to chinese ssec index abstract this paper presents the binomial markov switching multifractal bmsm model of asset returns with skewed t innovations bmsm skewed t for short which considers the fat tails skewness and multifractality in asset returns simultaneously the parameters of bmsm skewed t model can be estimated by maximum likelihood ml methods and volatility forecasting can be accomplished via bayesian updating in order to evaluate the performance of bmsm skewed t model bmsm model with normal innovations bmsm n bmsm model with student t innovations bmsm t and garch 1 1 models garch n garch t and garch skewed t are chosen for comparison through empirical studies on shanghai stock exchange composite index ssec we find that for sample estimation bmsm models outperform the garch 1 1 models through bic and aic rules and bmsm skewed t performs the best among all the models due to its fat tails skewness and multifractality in addition bmsm skewed t model dominates other models at most forecasting horizons for out of sample volatility forecasts in terms of mse mae and spa test

nonparametric time variant frequency response function estimates using arbitrary excitations the time variant frequency response function tv frf uniquely characterises the dynamic behaviour of a linear time variant ltv system this paper proposes a method for estimating nonparametrically the dynamic part of the tv frf from known input noisy output observations the arbitrary time variation of the tv frf is modelled by legendre polynomials in opposition to existing solutions the proposed method is applicable to arbitrary inputs

bayesian methods for hidden markov models markov chain monte carlo mcmc sampling strategies can be used to simulate hidden markov model hmm parameters from their posterior distribution given observed data some mcmc methods used in practice for computing likelihood conditional probabilities of hidden states and the most likely sequence of states can be improved by incorporating established recursive algorithms the most important of these is a set of forward backward recursions calculating conditional distributions of the hidden states given observed data and model parameters i show how to use the recursive algorithms in an mcmc context and demonstrate mathematical and empirical results showing a gibbs sampler using the forward backward recursions mixes more rapidly than another sampler often used for hmms iintroduce an augmented variables technique for obtaining unique state labels in hmms and finite mixture models i show how recursive computing allows the statistically efficient use of mcmc output when estimating the hidden states i

lap number properties for p laplacian problems investigated by lyapunov methods abstract in this work we consider a one dimensional quasilinear parabolic equation and we prove that the lap number of any solution cannot increase through orbits as the time passes if the initial data is a continuous function we deal with the lap number functional as a lyapunov function and apply lap number properties to reach an understanding on the asymptotic behavior of a particular problem

specification testing when score test statistics are identically zero we investigate the problem of previous specification testing when the score vector evaluated at the restricted mle is identically zero several econometric examples are provided a general test procedure which generalizes the geometric principle of the score test is proposed the wald and the likelihood ratio tests are also analyzed even under such irregularities the usual asymptotic distribution of the likelihood ratio statistics is still valid however the wald type statistics need to be modified the generalized score the likelihood ratio and the modified wald tests are shown to be asymptotically equivalent the asymptotic efficiency of the tests is derived

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