on theoretical pricing of options with fuzzy estimators in this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function using statistical data this application belongs to the financial field and especially to the section of financial engineering in financial markets there are great fluctuations thus the element of vagueness and uncertainty is frequent this application concerns theoretical pricing of options and in particular the black and scholes options pricing formula we make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number furthermore we apply the black and scholes formula by using adaptive fuzzy numbers introduced by thiagarajah et al k thiagarajah s s appadoo a thavaneswaran option valuation model with adaptive fuzzy numbers computers and mathematics with applications 53 2007 831 841 for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value we refer to both cases of call and put option prices according to the black scholes model and also analyze the results to greek parameters finally a numerical example is presented for both methods and a comparison is realized based on the results

optimality conditions for linear programming problems with fuzzy coefficients the optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers the solution concepts proposed in this paper will follow from the similar solution concept called the nondominated solution in the multiobjective programming problem under these settings the optimality conditions will be naturally elicited

pricing european options under uncertainty with application of levy processes and the minimal lq equivalent martingale measure abstract the study involves pricing of european options with usage of stochastic and fuzzy methods we use a geometric levy process as the model of the underlying asset assuming that the log price of a primary financial instrument is a jump diffusion with jump part described by a linear combination of time homogeneous poisson processes analytical option pricing formulas in crisp case using the minimal l q equivalent martingale measure are derived the pricing expressions are achieved employing probability and stochastic analysis the fuzzy counterparts of some model parameters are explored due to the fact that they are imprecisely evaluated applying fuzzy arithmetic we derive the analytical option pricing expressions with fuzzy parameters moreover we conceptualize a method of decision making taking into consideration the obtained fuzzy formulas at last we go through numerical examples to illustrate our theoretical results our main achievement in the paper is overcoming difficulties related to derivation of the option pricing formulas by advanced analysis of jacod grigelionis characteristics of the log price process used in our approach for the minimal l q equivalent martingale measure as well as the skilled use of fuzzy arithmetic methods

option valuation model with adaptive fuzzy numbers in this paper we consider moment properties for a class of quadratic adaptive fuzzy numbers defined in dubois and prade d dubois h prade fuzzy sets and systems theory and applications academic press new york 1980 the corresponding moments of trapezoidal fuzzy numbers tr f n s and triangular fuzzy numbers t f n s turn out to be special cases of the adaptive fuzzy number s bodjanova median value and median interval of a fuzzy number information sciences 172 2005 73 89 a numerical example is presented based on the black scholes option pricing formula with quadratic adaptive fuzzy numbers for the characteristics such as volatility parameter interest rate and stock price our approach hinges on a characterization of imprecision by means of fuzzy set theory

estimation of a fuzzy regression model using fuzzy distances regression analysis is a powerful statistical tool that has many applications in different areas the problem of regression analysis under a fuzzy environment has been treated in the literature from different points of view and considering a variety of input output data crisp or fuzzy however we realize that in general most research papers have a conflict between the solution of the fuzzy regression problem using crisp distances minimizing a real error function and the interpretation of fuzzy data as possibility distributions the main aim of this paper is to develop a methodology to solve this problem introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers the new approach allows us to obtain linear and nonlinear models that reach the lowest fuzzy error the estimation process in general can be considered easier to apply in practice and it is not limited to triangular fuzzy numbers numerical examples are provided to illustrate the usefulness and applicability of these results and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory

application of levy processes and esscher transformed martingale measures for option pricing in fuzzy framework in this paper we consider the european option valuation problem we assume that the underlying asset follows a geometric levy process the log price is a sum of a brownian motion with drift and a linear combination of poisson processes describing jumps in price in our approach we use martingale method and theory of fuzzy sets to obtain the european call and put option pricing formulas we use the mean correcting and the esscher transformed martingale measures application of the first mentioned measure required deep analysis of transformation of characteristics of levy process we assume that some model parameters cannot be precisely described and therefore we apply fuzzy numbers application of fuzzy arithmetic enables us to consider different sources of uncertainty and introduce experts opinions or imprecise estimates to the model in contradistinction to our previous papers where the european call option price at time zero was analysed we introduce the valuation expressions of the european call and put options for arbitrary time t numerical simulations conducted in the paper are used to analyse and illustrate the theoretical results this numerical approach is based on l r numbers and the exact shape of the fuzzy numbers which give us the possibility of comparing behaviour of option prices for various values of the parameters of the underlying asset

stability analysis of neutral type systems in hilbert space the asymtoptic stability properties of neutral type systems are studied mainly in the critical case when the exponential stability is not possible we consider an operator model of the system in hilbert space and use recent results on the existence of a riesz basis of invariant finite dimensional subspaces in order to verify its dissipativity the main results concern the conditions of asymptotic non exponential stability we show that the property of asymptotic stability is not determinated only by the spectrum of the system but essentially depends on the geometric spectral characteristic of its main neutral term moreover we present an example of two systems of neutral type which have both the same spectrum in the open left half plane and the main neutral term but one of them is asymptotically stable while the other is unstable

exact observability and controllability for linear neutral type systems the problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach the duality with the exact controllabil ity problem is the main tool it is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system a nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator the characterization of the duality between controllability and observability is deduced and then observability conditions are obtained

on stabilization by state feedback for neutral differential difference equations in this paper we consider a class of feedback operators for a linear differential difference equation of the neutral type we show that if a system has unstable neutral root chains any stabilizing feedback operator in this class must contain a derivative of the delayed state component under the assumption of exact controllability we construct a stabilizing feedback operator

option pricing with application of levy processes and the minimal variance equivalent martingale measure under uncertainty this paper is dedicated to european option pricing under assumption that the underlying asset follows a geometric levy process the log price of a primary financial instrument has the form of a sum of a drift component a brownian component and a linear combination of time homogeneous poisson processes modeling jumps in price in our approach we apply stochastic analysis especially the change of probability measure techniques as well as fuzzy sets theory to obtain the option valuation formulas we use the minimal variance equivalent martingale measure which requires an advanced analysis of transformation of levy characteristic triplets we obtain analytical option valuation expressions in crisp case moreover we assume that some model parameters are described in an imprecise way and therefore we use their fuzzy counterparts applying fuzzy arithmetic we take into account various types of uncertainty on the market as a result we obtain the analytical option pricing formulas with fuzzy parameters we also propose a method of automatized decision making which utilizes the fuzzy valuation formulas apart from the general pricing expressions we provide numerical examples to illustrate our theoretical results

set valued choquet integrals revisited this paper performs a further investigation on the set valued choquet integral given by jang and kwon fuzzy sets and systems 112 2000 233 some incorrect properties are revised it is pointed out that the definition for convergence of sequence of sets or set valued functions is unreasonable by using the usual kuratowski s convergence some new convergence theorems for the set valued choquet integral are shown meanwhile some other properties are obtained

on strong regular stabilizability for linear neutral type systems the problem of strong stabilizability of linear systems of neutral type is investigated we are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts this is the case when the main part of the neutral equation is not assumed to be stable in the classical sense we discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls the method covers the case of multivariable control and is essentially based on the idea of infinite dimensional pole assignment proposed in g m sklyar a v rezounenko a theorem on the strong asymptotic stability and determination of stabilizing controls c r acad sci paris ser i math 333 8 2001 807 812 our approach is based on the recent results on the riesz basis of invariant finitedimensional subspaces and strong stability for neutral type systems presented in r rabah g m sklyar a v rezounenko stability analysis of neutral type systems in hilbert space j differential equations 214 2 2005 391 428

pcan probabilistic correlation analysis of two non normal data sets most cancer research now involves one or more assays profiling various biological molecules e g messenger rna and micro rna in samples collected on the same individuals the main interest with these genomic data sets lies in the identification of a subset of features that are active in explaining the dependence between platforms to quantify the strength of the dependency between two variables correlation is often preferred however expression data obtained from next generation sequencing platforms are integer with very low counts for some important features in this case the sample pearson correlation is not a valid estimate of the true correlation matrix because the sample correlation estimate between two features variables with low counts will often be close to zero even when the natural parameters of the poisson distribution are in actuality highly correlated we propose a model based approach to correlation estimation between two non normal data sets via a method we call probabilistic correlations analysis or pcan pcan takes into consideration the distributional assumption about both data sets and suggests that correlations estimated at the model natural parameter level are more appropriate than correlations estimated directly on the observed data we demonstrate through a simulation study that pcan outperforms other standard approaches in estimating the true correlation between the natural parameters we then apply pcan to the joint analysis of a microrna mirna and a messenger rna mrna expression data set from a squamous cell lung cancer study finding a large number of negative correlation pairs when compared to the standard approaches

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

option pricing under a double exponential jump diffusion model this paper aims to extend the analytical tractability of the black scholes model to alternative models with arbitrary jump size distributions more precisely we propose a jump diffusion model for asset prices whose jump sizes have a mixed exponential distribution which is a weighted average of exponential distributions but with possibly negative weights the new model extends existing models such as hyperexponential and double exponential jump diffusion models because the mixed exponential distribution can approximate any distribution as closely as possible including the normal distribution and various heavy tailed distributions the mixed exponential jump diffusion model can lead to analytical solutions for laplace transforms of prices and sensitivity parameters for path dependent options such as lookback and barrier options the laplace transforms can be inverted via the euler inversion algorithm numerical experiments indicate that the formulae are easy to implement and accurate the analytical solutions are made possible mainly because we solve a high order integro differential equation explicitly a calibration example for spy options shows that the model can provide a reasonable fit even for options with very short maturity such as one day this paper was accepted by michael fu stochastic models and simulation

spectral assignment for neutral type systems and moment problems for a large class of linear neutral type systems the problem of assigning eigenvalues and eigenvectors is investigated i e finding the system that has the given spectrum and in some sense allmost all eigenvectors the solution of this problem enables vector moment problems to be considered using the construction of a neutral type system the exact controllability property of the system obtained gives the solution of the vector moment problem

sparse semiparametric canonical correlation analysis for data of mixed types summarycanonical correlation analysis investigates linear relationships between two sets of variables but it often works poorly on modern datasets because of high dimensionality and mixed data types such as continuous binary and zero inflated to overcome these challenges we propose a semiparametric approach to sparse canonical correlation analysis based on the gaussian copula the main result of this paper is a truncated latent gaussian copula model for data with excess zeros which allows us to derive a rank based estimator of the latent correlation matrix for mixed variable types without estimation of marginal transformation functions the resulting canonical correlation analysis method works well in high dimensional settings as demonstrated via numerical studies and when applied to the analysis of association between gene expression and microrna data from breast cancer patients

the analysis of exact controllability of neutral type systems by the moment problem approach the problem of exact null controllability is considered for a wide class of linear neutral type systems with distributed delay the main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families a complete characterization of this problem is given the minimal time of controllability is specified the results are based on the analysis of the riesz basis property of eigenspaces of the neutral type systems in hilbert space

high dimensional semiparametric latent graphical model for mixed data summary we propose a semiparametric latent gaussian copula model for modelling mixed multivariate data which contain a combination of both continuous and binary variables the model assumes that the observed binary variables are obtained by dichotomizing latent variables that satisfy the gaussian copula distribution the goal is to infer the conditional independence relationship between the latent random variables based on the observed mixed data our work has two main contributions we propose a unified rank based approach to estimate the correlation matrix of latent variables we establish the concentration inequality of the proposed rank based estimator consequently our methods achieve the same rates of convergence for precision matrix estimation and graph recovery as if the latent variables were observed the methods proposed are numerically assessed through extensive simulation studies and real data analysis

hukuhara derivative of the fuzzy expected value in this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its hukuhara derivative with respect to the parameter main results are obtained for two different sets of general conditions one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from and the second one just requiring conditions over the projections of the fuzzy random variables

the nonparanormal semiparametric estimation of high dimensional undirected graphs recent methods for estimating sparse undirected graphs for real valued data in high dimensional problems rely heavily on the assumption of normality we show how to use a semiparametric gaussian copula or nonparanormal for high dimensional inference just as additive models extend linear models by replacing linear functions with a set of one dimensional smooth functions the nonparanormal extends the normal by transforming the variables by smooth functions we derive a method for estimating the nonparanormal study the method s theoretical properties and show that it works well in many examples

minimax estimation in sparse canonical correlation analysis canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables this paper considers the problem of estimating the leading canonical correlation directions in high dimensional settings recently under the assumption that the leading canonical correlation directions are sparse various procedures have been proposed for many high dimensional applications involving massive data sets however there has been few theoretical justification available in the literature in this paper we establish rate optimal nonasymptotic minimax estimation with respect to an appropriate loss function for a wide range of model spaces two interesting phenomena are observed first the minimax rates are not affected by the presence of nuisance parameters namely the covariance matrices of the two sets of random variables though they need to be estimated in the canonical correlation analysis problem second we allow the presence of the residual canonical correlation directions however they do not influence the minimax rates under a mild condition on eigengap a generalized sin theta theorem and an empirical process bound for gaussian quadratic forms under rank constraint are used to establish the minimax upper bounds which may be of independent interest

degrees of freedom in lasso problems we derive the degrees of freedom of the lasso fit placing no assumptions on the predictor matrix x like the well known result of zou et al 2007 which gives the degrees of freedom of the lasso fit when x has full column rank we express our result in terms of the active set of a lasso solution we extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitrary predictor matrix x and an arbitrary penalty matrix d though our focus is degrees of freedom we establish some intermediate results on the lasso and generalized lasso that may be interesting on their own

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

a unified approach to asymptotic behaviors for the autoregressive model with fuzzy data we propose a unified estimator for the autoregressive model with fuzzy input output variables based on the least squares method the least squares estimation is investigated in presence of a unified r distance defined on the space of fuzzy numbers we investigate asymptotic properties of the unified estimator under some simple conditions as well as a generalization which reduces to the asymptotic properties under those distances when the distances are the special cases of r distance some simulation studies are included to compare the asymptotic properties of estimators formed under several distances being the special cases of r distance