estimating the ultimate bound and positively invariant set for the lorenz system and a unified chaotic system to estimate the ultimate bound and positively invariant set for a dynamic system is an important but quite challenging task in general in this paper we attempt to investigate the ultimate bound and positively invariant set for two specific systems the lorenz system and a unified chaotic system we derive an ellipsoidal estimate of the ultimate bound and positively invariant set for the lorenz system for all the positive values of its parameters a b and c and obtain the minimum value of volume for the ellipsoid comparing with the best results in the current literature d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 our new results fill up the gap of the estimate for the cases of 0 a 1 and 0 b 2 x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 furthermore the estimation derived here contains the results given in d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 and x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 as special cases along the same line we also provide estimates of cylindrical and ellipsoidal bounds for a unified chaotic system for its parameter range 0 129 and obtain the minimum value of volume for the ellipsoid the estimate is more accurate than and also extends the result of d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 and x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

a hyperchaotic system from the rabinovich system this paper presents a new 4d hyperchaotic system which is constructed by a linear controller to the 3d rabinovich chaotic system some complex dynamical behaviors such as boundedness chaos and hyperchaos of the 4d autonomous system are investigated and analyzed a theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a lienard like oscillatory motion around a hypersaddle stationary point at the origin the corresponding bounded hyperchaotic and chaotic attractors are first numerically verified through investigating phase trajectories lyapunov exponents bifurcation path and poincare projections finally two complete mathematical characterizations for 4d hopf bifurcation are rigorously derived and studied

bifurcations of the von karman equations with robin boundary conditions abstract we study buckling of a rectangular plate with elastic support and restraint along two edges and simple support along the other two edges this corresponds to a bifurcation analysis of the von karman equations with robin boundary conditions of special interest is the phenomenon of mode jumping in deformation of the plate we discretize the von karman equations with the finite difference methods the solution curves branching from the first two simple bifurcation points resulted from splitting of a double bifurcation point are numerically traced with respect to the increase of the load by using the continuation methods our numerical results show that mode jumping depends on length of the plate and stiffness of the elastic support

some computational aspects of the stability analysis of nonlinear structures abstract the perturbation method and the continuation method are the two most popular techniques for the solution of finite element equations that describe instability phenomena this paper presents a summary of the principles involved and describes some trends in the development of these techniques

estimation of risk neutral densities using positive convolution approximation this paper proposes a new nonparametric method for estimating the conditional risk neutral density rnd from a cross section of option prices the idea of the method is to t option prices by nding the optimal density in a special admissible set the admissible set consists of functions each of which may be represented as a convolution of a positive kernel with another density the method is termed the positive convolution approximation pca the important properties of pca are that it 1 is completely agnostic about the data generating process 2 controls against over tting while allowing for small samples 3 always produces arbitragefree estimators and 4 is computationally simple in a monte carlo experiment pca is compared to several popular methods mixtures of lognormals with one two and three lognormals hermite polynomials two regularization methods for the rnd and for implied volatilities and sigma shape polynomials pca is found to be a promising alternative to the competitors c 2003 elsevier b v all rights reserved

parametric option pricing a divide and conquer approach abstract non parametric option pricing models such as artificial neural networks are often found to outperform their parametric counterparts in empirical option pricing exercises in this context non parametric models are viewed as more flexible and amenable to adaptive learning however the main drawback of non parametric approaches is their lack of stability which is detrimental to out of sample performance this is the key reason why one may prefer a parsimonious parametric model this paper proposes a parametric takagi sugeno kang tsk fuzzy rule based option pricing model that requires only a small number of rules to describe highly complex non linear functions the findings for this data driven approach indicate that the tsk model presents a robust option pricing tool that is superior to an array of well known parametric models from the literature in addition its predictive performance is consistently no worse than that of a non parametric feedforward neural network model

non parametric extraction of implied asset price distributions abstract we present a fully non parametric method for extracting risk neutral densities rnds from observed option prices the aim is to obtain a continuous smooth monotonic and convex pricing function that is twice differentiable thus irregularities such as negative probabilities that afflict many existing rnd estimation techniques are reduced our method employs neural networks to obtain a smoothed pricing function and a central finite difference approximation to the second derivative to extract the required gradients this novel technique was successfully applied to a large set of ftse 100 daily european exercise esx put options data and as an ansatz to the corresponding set of american exercise sei put options the results of paired t tests showed significant differences between rnds extracted from esx and sei option data reflecting the distorting impact of early exercise possibility for the latter in particular the results for skewness and kurtosis suggested different shapes for the rnds implied by the two types of put options however both esx and sei data gave an unbiased estimate of the realised ftse 100 closing prices on the options expiration date we confirmed that estimates of volatility from the rnds of both types of option were biased estimates of the realised volatility at expiration but less so than the liffe tabulated at the money implied volatility

semi nonparametric estimation of the call option price surface under strike and time to expiry no arbitrage constraints abstract we suggest a semi nonparametric estimator for the call option price surface the estimator is a bivariate tensor product b spline to enforce no arbitrage constraints across strikes and expiry dates we establish sufficient no arbitrage conditions on the control net of the b spline surface the conditions are linear and therefore allow for an implementation of the estimator by means of standard quadratic programming techniques the consistency of the estimator is proved by means of simulations we explore the statistical efficiency benefits that are associated with estimating option price surfaces and state price densities under the full set of no arbitrage constraints we estimate a call option price surface families of first order strike derivatives and state price densities for s p 500 option data

functional linear regression with functional response abstract in this paper we develop new estimation results for functional regressions where both the regressor z t and the response y t are functions of hilbert spaces indexed by the time or a spatial location the model can be thought as a generalization of the multivariate regression where the regression coefficient is now an unknown operator we propose to estimate the operator by tikhonov regularization which amounts to apply a penalty on the l 2 norm of we derive the rate of convergence of the mean square error the asymptotic distribution of the estimator and develop tests on as trajectories are often not fully observed we consider the scenario where the data become more and more frequent infill asymptotics we also address the case where z is endogenous and instrumental variables are used to estimate an application to the electricity consumption completes the paper

recovering risk neutral probability density functions from options prices using cubic splines and ensuring nonnegativity abstract we present a new approach to estimate the risk neutral probability density function pdf of the future prices of an underlying asset from the prices of options written on the asset the estimation is carried out in the space of cubic spline functions yielding appropriate smoothness the resulting optimization problem used to invert the data and determine the corresponding density function is a convex quadratic or semidefinite programming problem depending on the formulation both of these problems can be efficiently solved by numerical optimization software in the quadratic programming formulation the positivity of the risk neutral pdf is heuristically handled by posing linear inequality constraints at the spline nodes in the other approach this property of the risk neutral pdf is rigorously ensured by using a semidefinite programming characterization of nonnegativity for polynomial functions we tested our approach using data simulated from black scholes option prices and using market data for options on the s p 500 index the numerical results we present show the effectiveness of our methodology for estimating the risk neutral probability density function

a hyperchaos generated from lorenz system abstract this paper presents a four dimension hyperchaotic lorenz system obtained by adding a nonlinear controller to lorenz chaotic system the hyperchaotic lorenz system is studied by bifurcation diagram lyapunov exponents spectrum and phase diagram numerical simulations show that the new system s behavior can be convergent divergent periodic chaotic and hyperchaotic when the parameter varies

bifurcation hierarchy of a rectangular plate abstract the mechanism of the complex recursive bifurcation behavior of a four sides simply supported rectangular plate is investigated such complex behavior is due to the hidden symmetry of the plate associated with the periodic nature of the solutions the group theoretic bifurcation theory is employed to arrive at a lattice of subgroups which expresses the rule for the behavior this rule is shown to suffer degeneration due to the restriction by the boundaries compared with that of geometrical symmetry the governing equation of this plate is discretized by means of galerkin s method with the use of the double fourier series as shape functions the tangential stiffness matrix of the plate is shown to be block diagonalized by appropriately permuting the order of the fourier series following the rule presented the bifurcation analysis of the plate is carried out to assess the validity of the rule and to demonstrate the merit of the block diagonalization as a result of this the vital role of the bifurcation rule in the proper understanding and successful analysis of the complex bifurcation behavior has been demonstrated

branch switching for pitchfork bifurcation in nonlinear finite element method a general branch switching approach is proposed based on pseudo arc length continuation in the nonlinear finite element method fem to trace the branch solution curve at the pitchfork bifurcation point in parameter space by this approach branch direction can be determined without derivatives of tangent stiffness matrix this approach is proved mathematically and is inserted into a general fem code stability of equilibrium corresponding to each solution curve is estimated by the lagrange dirichlet criteria as an example the whole process of the elastic mode jumping for rectangular thin plates in which there are many pitchfork bifurcations in parameter space in loading and unloading is simulated by the improved fem code the numerical results are identical with that of an experiment done by previous researchers

nonparametric option pricing under shape restrictions frequently economic theory places shape restrictions on functional relationships between economic variables this paper develops a method to constrain the values of the first and second derivatives of nonparametric locally polynomial estimators we apply this technique to estimate the state price density spd or risk neutral density implicit in the market prices of options the option pricing function must be monotonic and convex simulations demonstrate that nonparametric estimates can be quite feasible in the small samples relevant for day to day option pricing once appropriate theory motivated shape restrictions are imposed using s p 500 option prices we show that unconstrained nonparametric estimators violate the constraints during more than half the trading days in 1999 unlike the constrained estimator we propose

some computational aspects of a group theoretic finite element approach to the buckling and postbuckling analyses of plates and shells of revolution abstract progress in the application of group theoretic methods to the nonlinear bifurcation analysis of symmetric structures has provided new hope in understanding the global postbuckling behavior of symmetric thin shell structures however what is still lacking in the computational mechanics community is a general purpose fe code with a group theoretic capability designed to take optimal advantage of existing symmetry this paper addresses some of the important issues associated with developing such a code the long term goal being to provide structural analysts with new numerical tools for doing careful global analyses of imperfection sensitive structures which may eventually lead to more accurate predictions of the maximum load carrying capacity of thin imperfection sensitive shell structures

a bayesian approach to bandwidth selection for multivariate kernel regression with an application to state price density estimation abstract this paper presents a bayesian approach to bandwidth selection for multivariate kernel regression a monte carlo study shows that under the average squared error criterion the bayesian bandwidth selector is comparable to the cross validation method and clearly outperforms the bootstrapping and rule of thumb bandwidth selectors the bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state price density of arrow debreu securities with the s p 500 index options data and the dax index options data the proposed bayesian bandwidth selector represents a data driven solution to the problem of choosing bandwidths for the multivariate kernel regression involved in the nonparametric estimation of the state price density pioneered by ait sahalia and lo ait sahalia y lo a w 1998 nonparametric estimation of state price densities implicit in financial asset prices the journal of finance 53 499 547

dynamics of state price densities abstract state price densities spds are an important element in applied quantitative finance in a black scholes world they are lognormal distributions but in practice volatility changes and the distribution deviates from log normality in order to study the degree of this deviation we estimate spds using eurex option data on the dax index via a nonparametric estimator of the second derivative of the european call pricing function the estimator is constrained so as to satisfy no arbitrage constraints and corrects for the intraday covariance structure in option prices in contrast to existing methods we do not use any parametric or smoothness assumptions

pricing and hedging derivative securities with neural networks and a homogeneity hint abstract we estimate a generalized option pricing formula that has a functional shape similar to the usual black scholes formula by a feedforward neural network model this functional shape is obtained when the option pricing function is homogeneous of degree one with respect to the underlying asset price st and the strike price k we show that pricing accuracy gains can be made by exploiting this generalized black scholes shape instead of setting up a learning network mapping the ratio st k and the time to maturity directly into the derivative price we break down the pricing function into two parts one controlled by the ratio st k the other one by a function of time to maturity the results indicate that the homogeneity hint always reduces the out of sample mean squared prediction error compared with a feedforward neural network with no hint both feedforward network models with and without the hint provide similar delta hedging errors that are small relative to the hedging performance of the black scholes model however the model with hint produces a more stable hedging performance

a hyperchaotic system from a chaotic system with one saddle and two stable node foci this paper presents a 4d new hyperchaotic system which is constructed by a linear controller to a 3d new chaotic system with one saddle and two stable node foci some complex dynamical behaviors such as ultimate boundedness chaos and hyperchaos of the simple 4d autonomous system are investigated and analyzed the corresponding bounded hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories lyapunove exponents bifurcation path analysis of power spectrum and poincare projections finally two complete mathematical characterizations for 4d hopf bifurcation are rigorous derived and studied

shape constrained risk neutral density estimation by support vector regression abstract options are believed to have the function of reflecting market expectations on future underlying movements through its implicit risk neutral density rnd however it is not easy to obtain a well behaved rnd due to the data limitations the complex constraints and the ill posedness of the problem in this paper we propose a more effective nonparametric method for estimating the rnd from a set of european option bid ask quotes based on a linear programming support vector regression lpsvr the method allows us to fit beyond the range of data and to incorporate all the shape constraints and it thus always gives an arbitrage free density with full tails in addition the method does not need preprocessing of the data and is robust to the bid ask spread the monte carlo simulations and the empirical tests have been carried out to demonstrate the excellent accuracy and stability of the method the results show that the lpsvr method is a promising alternative for estimating the rnd