iterative weighted maximum likelihood denoising with probabilistic patch based weights image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation this paper presents a new approach for image denoising in the case of a known uncorrelated noise model the proposed filter is an extension of the nonlocal means nl means algorithm introduced by buades which performs a weighted average of the values of similar pixels pixel similarity is defined in nl means as the euclidean distance between patches rectangular windows centered on each two pixels in this paper a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model the denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data driven way these weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate we show that this iterative process noticeably improves the denoising performance especially in the case of low signal to noise ratio images such as synthetic aperture radar sar images numerical experiments illustrate that the technique can be successfully applied to the classical case of additive gaussian noise but also to cases such as multiplicative speckle noise the proposed denoising technique seems to improve on the state of the art performance in that latter case

maximum likelihood estimation of rician distribution parameters the problem of parameter estimation from rician distributed data e g magnitude magnetic resonance images is addressed the properties of conventional estimation methods are discussed and compared to maximum likelihood ml estimation which is known to yield optimal results asymptotically in contrast to previously proposed methods ml estimation is demonstrated to be unbiased for high signal to noise ratio snr and to yield physical relevant results for low snr

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

on consistency of stochastic dominance and mean semideviation models we analyze relations between two methods frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches new necessary conditions for stochastic dominance are developed these conditions compare values of a certain functional which contains two components the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree if the weight of the semideviation in the composite objective does not exceed the weight of the expected value maximization of such a functional yields solutions which are efficient in terms of stochastic dominance the results are illustrated graphically

conditionally evenly convex sets and evenly quasi convex maps abstract evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces we introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem this notion is then applied to obtain the dual representation of conditionally evenly quasi convex maps which turns out to be a fundamental ingredient in the study of quasi convex dynamic risk measures

measures of residual risk with connections to regression risk tracking surrogate models and ambiguity measures of residual risk are developed as an extension of measures of risk they view a random variable of interest in concert with an auxiliary random vector that helps to manage predict and mitigate the risk in the original variable residual risk can be exemplified as a quantification of the improved situation faced by a hedging investor compared to that of a single asset investor but the notion reaches further with deep connections emerging with forecasting and generalized regression we establish the fundamental properties in this framework and show that measures of residual risk along with generalized regression can play central roles in the development of risk tuned approximations of random variables in tracking of statistics and in estimation of the risk of conditional random variables the paper ends with dual expressions for measures of residual risk which lead to further insights and a new class of distributionally robust optimization models

suitability of upwind biased finite difference schemes for large eddy simulation of turbulent flows we have simulated flow past a circular cylinder at a reynolds number of 3 9 x 10 3 using a solver that employs an energy conservative second order central difference scheme for spatial discretization detailed comparisons of turbulence statistics and energy spectra in the downstream wake region 7 0 x d 10 0 have been made with the results of beaudan and moin and with experiments to assess the impact of numerical diffusion on the flowfield based on these comparisons conclusions are drawn on the suitability of higher order upwind schemes for les in complex geometries

portfolio selection problem with value at risk constraints under non extensive statistical mechanics the optimal portfolio selection problem is a major issue in the financial field in which the process of asset prices is usually modeled by a wiener process that is the return distribution of the asset is normal however several empirical results have shown that the return distribution of the asset has the characteristics of fat tails and aiguilles and is not normal in this work we propose an optimal portfolio selection model with a value at risk var constraint in which the process of asset prices is modeled by the non extensive statistical mechanics instead of the classical wiener process the model can describe the characteristics of fat tails and aiguilles of returns using the dynamic programming principle we derive a hamilton jacobi bellman hjb equation then employing the lagrange multiplier method we obtain closed form solutions for the case of logarithmic utility moreover the empirical results show that the price process can more accurately fit the empirical distribution of returns than the familiar wiener process in addition as the time increases the constraint becomes binding that is to control the risk the agent reduces the proportion of the wealth invested in the risky asset furthermore at the same confidence level the agent reduces the proportion of the wealth invested in the risky asset more quickly under our model than under the model based on the wiener process this can give investors a good decision making reference

efficient hedging with coherent risk measure abstract the idea of efficient hedging has been introduced by follmer and leukert they defined the shortfall risk as the expectation of the shortfall weighted by a loss function and looked for strategies that minimize the shortfall risk under a capital constraint in this paper to measure the shortfall risk we use the coherent risk measures introduced by artzner delbaen eber and heath we show that for a given contingent claim h the optimal strategy consists in hedging a modified claim h for some randomized test this is an analogue of the results by follmer and leukert

optimization of convex risk functions we consider optimization problems involving convex risk functions by employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models and optimality and duality theory for problems with convex risk functions

multi period semi variance portfolio selection model and numerical solution variance is substituted by semi variance in markowitz s portfolio selection model moreover one period portfolio selection is extended to multi period in this paper a class of multi period semi variance model is formulated originally besides a hybrid genetic algorithm ga which makes use of the position displacement strategy of the particle swarm optimizer pso as a mutation operation is applied to solve the multi period semi variance model for this class of portfolio model numerical results show that the hybrid ga with pso is effective and feasible

impact of foreign exchange rate on oil companies risk in stock market during the recent years the importance of effective risk management has become extremely crucial value at risk var is a standard downside measure to explain the behavior of financial series as the garch models have been successfully applied in modeling the volatility structure of securities and other financial assets the var of garch models has turned into an important quantity to study in addition to garch family models the markov regime switching garch mrs garch models are a widely used approach to model financial volatility with potential structural breaks in this paper we evaluated the performance of the mrs garch models with the traditional arma garch family models for estimating var of the stock return of operating companies in the oil industry srocoi in irans stock market under the normal student t and ged distributions our findings showed that the mrs garch models outperform the arma garch family models to capture the characteristics of the srocois volatility additionally we evaluated impact of the foreign exchange rate fluctuations on the var of srocois that were calculated from the optimal models under two regimes usingardl model the results further demonstrated that foreign exchange rate fluctuations have significant and different impacts on the var of srocois across regimes we modeled srocois in irans stock market using mrs garch and arma garch family models mrs garch models under student t and ged distributions have better performance to capture srocois we estimated in sample and out of sample var of srocois from optima models we evaluated impact of the foreign exchange rate fluctuations on the var of srocois foreign exchange rate significantly effect on the var of srocois in different regimes

on the uncertainty of var of individual risk abstract value at risk var is a prevalent risk measure used in financial risk management the calculation of var relies on the distribution of the potential loss position which is generally unknown in practice in this article we introduce a model of uncertainty for the distribution of a loss variable and investigate the effect on var using a worst scenario approach the proposed model is flexible and can be applied to various types of distributions the robust var and an associated worst scenario measure are identified it is shown that the choice of the loss model is still important when there is an uncertainty model

portfolio selection based on a benchmark process with dynamic value at risk constraints abstract portfolio selection is an essential issue in finance it studies how to allocate one s wealth in a basket of securities to maximize the return and minimize the risk and dynamic portfolio selection based on a benchmark process is one of the most important types different from the existing literature we impose a dynamic risk control on it as a matter of fact performing an optimal portfolio strategy in the light of a dynamic portfolio formulation does not eliminate the possibility of an investor going to bankruptcy or even more serious situations in a volatile financial market before the terminal time so it is reasonable and necessary to impose a dynamic risk control on the instantaneous wealth throughout the investment horizon to ensure that the investment behavior can proceed and we intend to address this interesting issue in this paper more specifically we investigate the dynamic portfolio selection problem based on a benchmark process coupled with a dynamic value at risk constraint by stochastic dynamic programming techniques we derive the corresponding hamilton jacobi bellman equation moreover the optimal portfolio strategies are obtained by lagrange multiplier method to verify the model two numerical examples are illustrated the results show the difference of optimal portfolio strategies with and without the dynamic var constraint the composition of the risky assets is constant but the investment proportion is reduced as the var constraint becomes binding this research can provide a good decision making reference for risk averse investors

robustness of optimal portfolios under risk and stochastic dominance constraints abstract solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation estimation and incomplete information the obtained results recommendations for the risk and portfolio manager should be then carefully analyzed we shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity based global contamination bounds results obtained in our paper dupacova j kopa m 2012 robustness in stochastic programs with risk constraints annals of operations research 200 55 74 were derived for the risk and second order stochastic dominance constraints under suitable smoothness and or convexity assumptions that are fulfilled e g for the markowitz mean variance model in this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints local bounds for problems of a special structure are obtained under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test

a nonlocal maximum likelihood estimation method for rician noise reduction in mr images postacquisition denoising of magnetic resonance mr images is of importance for clinical diagnosis and computerized analysis such as tissue classification and segmentation it has been shown that the noise in mr magnitude images follows a rician distribution which is signal dependent when signal to noise ratio snr is low it is particularly difficult to remove the random fluctuations and bias introduced by rician noise the objective of this paper is to estimate the noise free signal from mr magnitude images we model images as random fields and assume that pixels which have similar neighborhoods come from the same distribution we propose a nonlocal maximum likelihood nlml estimation method for rician noise reduction our method yields an optimal estimation result that is more accurate in recovering the true signal from rician noise than nl means algorithm in the sense of snr contrast and method error we demonstrate that nlml performs better than the conventional local maximum likelihood lml estimation method in preserving and defining sharp tissue boundaries in terms of a well defined sharpness metric while also having superior performance in method error

wavelet based rician noise removal for magnetic resonance imaging it is well known that magnetic resonance magnitude image data obey a rician distribution unlike additive gaussian noise rician noise is signal dependent and separating signal from noise is a difficult task rician noise is especially problematic in low signal to noise ratio snr regimes where it not only causes random fluctuations but also introduces a signal dependent bias to the data that reduces image contrast this paper studies wavelet domain filtering methods for rician noise removal we present a novel wavelet domain filter that adapts to variations in both the signal and the noise

a majorize minimize framework for rician and non central chi mr images the statistics of many mr magnitude images are described by the non central chi ncc family of probability distributions which includes the rician distribution as a special case these distributions have complicated negative log likelihoods that are nontrivial to optimize this paper describes a novel majorize minimize framework for ncc data that allows penalized maximum likelihood estimates to be obtained by solving a series of much simpler regularized least squares surrogate problems the proposed framework is general and can be useful in a range of applications we illustrate the potential advantages of the framework with real and simulated data in two contexts 1 mr image denoising and 2 diffusion profile estimation in high angular resolution diffusion mri the proposed approach is shown to yield improved results compared to methods that model the noise statistics inaccurately and faster computation relative to commonly used nonlinear optimization techniques

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

risk preferences and their robust representation to address the plurality of interpretations of the subjective notion of risk we describe it by means of a risk order and concentrate on the context invariant features of diversification and monotonicity our main results are uniquely characterized robust representations of lower semicontinuous risk orders on vector spaces and convex sets this representation covers most instruments related to risk and allows for a differentiated interpretation depending on the underlying context that is illustrated in different settings for random variables risk perception can be interpreted as model risk and we compute among others the robust representation of the economic index of riskiness for lotteries risk perception can be viewed as distributional risk and we study the value at risk for consumption patterns which excerpt an intertemporality dimension in risk perception we provide an interpretation in terms of discounting risk and discuss some examples

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

optimality conditions in portfolio analysis with general deviation measures optimality conditions are derived for problems of minimizing a general measure of deviation of a random variable with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments general measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs the optimality conditions are applied to characterize the generalized master funds which elsewhere have been developed in extending classical portfolio theory beyond the case of standard deviation the consequences are worked out for deviation based on conditional value at risk and its variants in particular

standard stochastic dominance abstract we propose a new stochastic dominance sd criterion based on standard risk aversion which assumes decreasing absolute risk aversion and decreasing absolute prudence to implement the proposed criterion we develop linear systems of optimality conditions for a given prospect relative to a discrete or polyhedral choice opportunity set in a general state space model an empirical application to historical stock market data shows that small loser stocks are more appealing to standard risk averters than the existing mean variance mv and higher order sd criteria suggest due to their upside potential depending on the assumed trading strategy and evaluation horizon accounting for standardness increases the estimated abnormal returns of these stocks by about 50 to 200 basis points per annum relative to mv and higher order sd criteria an analysis of the mv tangency portfolio shows that the opportunity cost of the mv approximation to direct utility maximization can be substantial

denoising functional mr images a comparison of wavelet denoising and gaussian smoothing we present a general wavelet based denoising scheme for functional magnetic resonance imaging fmri data and compare it to gaussian smoothing the traditional denoising method used in fmri analysis one dimensional wavelab thresholding routines were adapted to two dimensional 2 d images and applied to 2 d wavelet coefficients to test the effect of these methods on the signal to noise ratio snr we compared the snr of 2 d fmri images before and after denoising using both gaussian smoothing and wavelet based methods we simulated a fmri series with a time signal in an active spot and tested the methods on noisy copies of it the denoising methods were evaluated in two ways by the average temporal snr inside the original activated spot and by the shape of the spot detected by thresholding the temporal snr maps denoising methods that introduce much smoothness are better suited for low snrs but for images of reasonable quality they are not preferable because they introduce heavy deformations wavelet based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions we also performed statistical parametric mapping on the denoised simulated time series as well as on a real fmri data set false discovery rate control was used to correct for multiple comparisons the results show that the methods that produce smooth images introduce more false positives the less smoothing wavelet based methods although generating more false negatives produce a smaller total number of errors than gaussian smoothing or wavelet based methods with a large smoothing effect

higher degree stochastic dominance optimality and efficiency abstract we characterize a range of stochastic dominance sd relations by means of finite systems of convex inequalities for sd optimality of degree 1 to 4 and sd efficiency of degree 2 to 5 we obtain exact systems that can be implemented using linear programming or convex quadratic programming for sd optimality of degree five and higher and sd efficiency of degree six and higher we obtain necessary conditions we use separate model variables for the values of the derivatives of all relevant orders at all relevant outcome levels which allows for preference restrictions beyond the standard sign restrictions our systems of inequalities can be interpreted in terms of piecewise polynomial utility functions with a number of pieces that increases with the number of outcomes and the degree of sd an empirical study analyzes the relevance of higher order risk preferences for comparing a passive stock market index with actively managed stock portfolios in standard data sets from the empirical asset pricing literature

generalized convexity and concavity of the optimal value function in nonlinear programming in this paper we consider generalized convexity and concavity properties of the optimal value functionf for the general parametric optimization problemp of the form minxf x s t x r many results on convexity and concavity characterizations off were presented by the authors in a previous paper such properties off and the solution set maps form an important part of the theoretical basis for sensitivity stability and parametric analysis in mathematical optimization we give sufficient conditions for several types of generalized convexity and concavity off in terms of respective generalized convexity and concavity assumptions onf and convexity and concavity assumptions on the feasible region point to set mapr specializations of these results to the parametric inequality equality constrained nonlinear programming problem are provided

a cure for noisy magnetic resonance images chi square unbiased risk estimation in this paper we derive an unbiased expression for the expected mean squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi square random variable we then consider the task of denoising squared magnitude magnetic resonance mr image data which are well modeled as independent noncentral chi square random variables on two degrees of freedom we consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate one in the general context of undecimated filterbank transforms and the other in the specific case of the unnormalized haar wavelet transform the resultant algorithms are computationally tractable and improve upon most state of the art methods for both simulated and actual mr image data

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

noise estimation and reduction in magnetic resonance imaging using a new multispectral nonlocal maximum likelihood filter denoising of magnetic resonance mr images enhances diagnostic accuracy the quality of image manipulations such as registration and segmentation and parameter estimation the first objective of this paper is to introduce a new high performance nonlocal filter for noise reduction in mr image sets consisting of progressively weighted that is multispectral images this filter is a multispectral extension of the nonlocal maximum likelihood filter nlml performance was evaluated on synthetic and textit in vivo t 2 and t 1 weighted brain imaging data and compared to the nonlocal means nlm and its multispectral version that is ms nlm and the nonlocal maximum likelihood nlml filters visual inspection of filtered images and quantitative analyses showed that all filters provided substantial reduction of noise further as expected the use of multispectral information improves filtering quality in addition numerical and experimental analyses indicated that the new multispectral nlml filter ms nlml demonstrated markedly less blurring and loss of image detail than seen with the other filters evaluated in addition since noise standard deviation sd is an important parameter for all of these nonlocal filters a multispectral extension of the method of maximum likelihood estimation mle of noise amplitude is presented and compared to both local and nonlocal mle methods numerical and experimental analyses indicated the superior performance of this multispectral method for estimation of noise sd

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

differential equations connecting var and cvar abstract the value at risk var is a very important risk measure for practitioners supervisors and researchers many practitioners draw on var as a critical instrument in risk management and other actuarial financial problems while supervisors and regulators must deal with var due to the basel accords and solvency ii among other reasons from a theoretical point of view var presents some drawbacks overcome by other risk measures such as the conditional value at risk cvar var is neither differentiable nor sub additive because it is neither continuous nor convex on the contrary cvar satisfies all of these properties and this simplifies many analytical studies if var is replaced by cvar in this paper several differential equations connecting both var and cvar will be given they will allow us to address several important issues involving var with the help of the cvar properties this new methodology seems to be very efficient in particular a new var representation theorem may be found and optimization problems involving var or probabilistic constraints always have an equivalent differentiable optimization problem applications in var marginal var cvar and marginal cvar estimates will be addressed as well illustrative actuarial and financial examples will be likewise presented

portfolio choice and optimal hedging with general risk functions a simplex like algorithm abstract the minimization of general risk functions is becoming more and more important in portfolio choice theory and optimal hedging there are two major reasons firstly heavy tails and the lack of symmetry in the returns of many assets provokes that the classical optimization of the standard deviation may lead to dominated strategies from the point of view of the second order stochastic dominance secondly but not less important many institutional investors must respect legal capital requirements which may be more easily studied if one deals with a risk measure related to capital losses this paper proposes a new method to simultaneously minimize several general risk or dispersion measures the representation theorems of risk functions are applied to transform the general risk minimization problem in a minimax problem and later in a linear programming problem between infinite dimensional banach spaces then new necessary and sufficient optimality conditions are stated and a simplex like algorithm is developed the algorithm solves the dual problem and provides both optimal portfolios and their sensitivities the approach is general enough and does not depend on any particular risk measure but some of the most important cases are specially analyzed a final real data numerical example illustrates the practical performance of the proposed methodology

optimal investment problem under non extensive statistical mechanics abstract the optimal investment problem in which the asset price process is modeled by the non extensive statistical mechanics is studied in this paper by the methods of deterministic control and the dynamic programming we obtain the optimal strategy with logarithmic utility function power utility function and quadratic utility function respectively moreover the numerical results indicate that the optimal investment strategy is affected by the non extensive parameter the proportion invested in the risky asset decreases as the wealth increases under quadratic utility function but it remains unchanged under power utility and logarithmic utility function

tractable almost stochastic dominance abstract ll almost stochastic dominance ll asd is a relaxation of the stochastic dominance sd concept proposed by leshno and levy that explains more of realistic preferences observed in practice than sd alone does unfortunately numerical applications of this concept such as identifying if a given portfolio is efficient or determining a marketed portfolio that dominates a given benchmark are computationally prohibitive due to the structure of ll asd we propose a new almost stochastic dominance asd concept that is computationally tractable for instance a marketed dominating portfolio can be identified by solving a simple linear programming problem moreover the new concept performs well on all the intuitive examples from the literature and in some cases leads to more realistic predictions than the earlier concept we develop some properties of asd formulate efficient optimization models and apply the concept to analyzing investors preferences between bonds and stocks for the long run

on differential stability in stochastic programming in this paper optimal solutions of a stochastic programming problem are considered as functions of the underlying probability distribution their directional derivatives in the sense of g teaux are calculated by applying some recent results from the sensitivity analysis of nonlinear programs these derivatives are employed as a heuristic device in order to derive the asymptotic distribution of statistical estimators of the optimal solutions

on time stochastic dominance induced by mixed integer linear recourse in multistage stochastic programs abstract we propose in this work a new multistage risk averse strategy based on time stochastic dominance tsd along a given horizon it can be considered as a mixture of the two risk averse measures based on first and second order stochastic dominance constraints induced by mixed integer linear recourse respectively given the dimensions of medium sized problems augmented by the new variables and constraints required by this new risk measure it is unrealistic to solve the problem up to optimality by plain use of mip solvers in a reasonable computing time at least instead of it decomposition algorithms of some type should be used we present an extension of our branch and fix coordination algorithm so named bfc tsd where a special treatment is given to cross scenario group constraints that link variables from different scenario groups a broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies the performance of the new version of the bfc algorithm versus the plain use of a state of the art mip solver is also reported

short note a high order pade adi method for unsteady convection diffusion equations a high order alternating direction implicit adi method for computations of unsteady convection diffusion equations is proposed by using fourth order pade schemes for spatial derivatives the present scheme is fourth order accurate in space and second order accurate in time the solution procedure consists of a number of tridiagonal matrix operations which make the computation cost effective the method is unconditionally stable and shows higher accuracy and better phase and amplitude error characteristics than the standard second order adi method d w peaceman h h rachford jr the numerical solution of parabolic and elliptic differential equations journal of the society of industrial and applied mathematics 3 1959 28 41 and the fourth order adi scheme of karaa and zhang high order adi method for solving unsteady convection diffusion problem journal of computational physics 198 2004 1 9

var as the cvar sensitivity var minimization is a complex problem playing a critical role in many actuarial and financial applications of mathematical programming the usual methods of convex programming do not apply due to the lack of sub additivity the usual methods of differentiable programming do not apply either due to the lack of continuity taking into account that the cvar may be given as an integral of var one has that var becomes a first order mathematical derivative of cvar this property will enable us to give accurate approximations in var optimization since the optimization var and cvar will become quite closely related topics applications in both finance and insurance will be given

second order stochastic dominance constrained portfolio optimization theory and computational tests abstract due to the definition of second order stochastic dominance ssd in terms of utility theory portfolio optimization with ssd constraints is of major practical interest we contribute to the field in two ways first we present a self contained theory with some new results and new proofs of known results second we perform a set of tests for computational efficiency we provide new and simple arguments for the formulation of ssd constraints in a mathematical programming framework for many individuals an ssd constraint may seem too severe wherefore various relaxations assd have been proposed we introduce yet another relaxation directional ssd where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio optimal step size depends on individual preferences reflected by the objective function we compare computational efficiency of seven approaches for sd constrained portfolio problems including ssd and assd constrained cases

a multi block adi finite volume method for incompressible navier stokes equations in complex geometries an efficient second order accurate finite volume method is developed for a solution of the incompressible navier stokes equations on complex multi block structured curvilinear grids unlike in the finite volume or finite difference based alternating direction implicit adi methods where factorization of the coordinate transformed governing equations is performed along generalized coordinate directions in the proposed method the discretized cartesian form navier stokes equations are factored along curvilinear grid lines the new adi finite volume method is also extended for simulations on multi block structured curvilinear grids with which complex geometries can be efficiently resolved the numerical method is first developed for an unsteady convection diffusion equation then is extended for the incompressible navier stokes equations the order of accuracy and stability characteristics of the present method are analyzed in simulations of an unsteady convection diffusion problem decaying vortices flow in a lid driven cavity flow over a circular cylinder and turbulent flow through a planar channel numerical solutions predicted by the proposed adi finite volume method are found to be in good agreement with experimental and other numerical data while the solutions are obtained at much lower computational cost than those required by other iterative methods without factorization for a simulation on a grid with o 10 5 cells the computational time required by the present adi based method for a solution of momentum equations is found to be less than 20 of that required by a method employing a biconjugate gradient stabilized scheme

on a class of minimax stochastic programs for a particular class of minimax stochastic programming models we show that the problem can be equivalently reformulated into a standard stochastic programming problem this permits the direct use of standard decomposition and sampling methods developed for stochastic programming we also show that this class of minimax stochastic programs is closely related to a large family of mean risk stochastic programs where risk is measured in terms of deviations from a quantile

equilibrium routing under uncertainty we provide a brief introduction to the basic models used to describe traffic on congested networks both in urban transport and telecommunications we discuss traffic equilibrium models covering atomic and non atomic routing games with emphasis on situations where the travel times are subject to random fluctuations we use convex optimization to present the models in a unified framework that stresses the common underlying structures as a prototypical example of traffic equilibrium with elastic demands we discuss some models for routing and congestion control in telecommunications we also describe a class of stochastic dynamics that model the adaptive behavior of agents and which provides a plausible micro foundation for the equilibrium finally we present some recent ideas on how risk averse behavior might be incorporated in the equilibrium models

an immersed boundary method based on discrete stream function formulation for two and three dimensional incompressible flows an immersed boundary method is proposed in the framework of discrete stream function formulation for incompressible flows in order to impose the non slip boundary condition the forcing term is determined implicitly by solving a linear system the number of unknowns of the linear system is the same as that of the lagrangian points representing the body surface thus the extra cost in force calculation is negligible if compared with that in the basic flow solver in order to handle three dimensional flows at moderate reynolds numbers a parallelized flow solver based on the present method is developed using the domain decomposition strategy to verify the accuracy of the immersed boundary method proposed in this work flow problems of different complexity decaying vortices flows over stationary and oscillating cylinders and a stationary sphere and flow over low aspect ratio flat plate are simulated and the results are in good agreement with the experimental or computational data in previously published literatures

dual stochastic dominance and related mean risk models we consider the problem of constructing mean risk models which are consistent with the second degree stochastic dominance relation by exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions this allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation we also provide stochastic linear programming formulations of these models

worst case conditional value at risk with application to robust portfolio management this paper considers the worst case conditional value at risk cvar in the situation where only partial information on the underlying probability distribution is available the minimization of the worst case cvar under mixture distribution uncertainty box uncertainty and ellipsoidal uncertainty are investigated the application of the worst case cvar to robust portfolio optimization is proposed and the corresponding problems are cast as linear programs and second order cone programs that can be solved efficiently market data simulation and monte carlo simulation examples are presented to illustrate the proposed approach

minimizing measures of risk by saddle point conditions the minimization of risk functions is becoming a very important topic due to its interesting applications in mathematical finance and actuarial mathematics this paper addresses this issue in a general framework many types of risk function may be involved a general representation theorem of risk functions is used in order to transform the initial optimization problem into an equivalent one that overcomes several mathematical caveats of risk functions this new problem involves banach spaces but a mean value theorem for risk measures is stated and this simplifies the dual problem then optimality is characterized by saddle point properties of a bilinear expression involving the primal and the dual variable this characterization is significantly different if one compares it with previous literature furthermore the saddle point condition very easily applies in practice four applications in finance and insurance are presented

wavelet based fmri analysis 3 d denoising signal separation and validation metrics we present a novel integrated wavelet domain based framework w ica for 3 d denoising functional magnetic resonance imaging fmri data followed by source separation analysis using independent component analysis ica in the wavelet domain we propose the idea of a 3 d wavelet based multi directional denoising scheme where each volume in a 4 d fmri data set is sub sampled using the axial sagittal and coronal geometries to obtain three different slice by slice representations of the same data the filtered intensity value of an arbitrary voxel is computed as an expected value of the denoised wavelet coefficients corresponding to the three viewing geometries for each sub band this results in a robust set of denoised wavelet coefficients for each voxel given the de correlated nature of these denoised wavelet coefficients it is possible to obtain more accurate source estimates using ica in the wavelet domain the contributions of this work can be realized as two modules first in the analysis module we combine a new 3 d wavelet denoising approach with signal separation properties of ica in the wavelet domain this step helps obtain an activation component that corresponds closely to the true underlying signal which is maximally independent with respect to other components second we propose and describe two novel shape metrics for post ica comparisons between activation regions obtained through different frameworks we verified our method using simulated as well as real fmri data and compared our results against the conventional scheme gaussian smoothing spatial ica s ica the results show significant improvements based on two important features 1 preservation of shape of the activation region shape metrics and 2 receiver operating characteristic curves it was observed that the proposed framework was able to preserve the actual activation shape in a consistent manner even for very high noise levels in addition to significant reduction in false positive voxels

probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra we consider stochastic programming problems with probabilistic constraints involving random variables with discrete distributions they can be reformulated as large scale mixed integer programming problems with knapsack constraints using specific properties of stochastic programming problems and bounds on the probability of the union of events we develop new valid inequalities for these mixed integer programming problems we also develop methods for lifting these inequalities these procedures are used in a general iterative algorithm for solving probabilistically constrained problems the results are illustrated with a numerical example

decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance abstract a problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered a number of choice rules are proposed and their main properties are investigated focusing particularly on the generalizations of stochastic dominance and statistical preference the particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered

computational methodology for large eddy simulation of tip clearance flows a large eddy simulation based flow solver that combines an immersed boundary technique with a curvilinear structured grid has been developed to study the temporal and spatial dynamics of an incompressible rotor tipclearance flow the overall objective of these simulations is to determine the underlying mechanisms for lowpressure fluctuations downstream of the rotor near the end wall salient features of the numerical methodology including the mesh topology the immersed boundary method the treatment of numerical instability for nondissipative schemes on highly skewed meshes and the parallelization of the code for shared memory computer platforms are discussed the computational approach is shown to be capable of capturing the evolution of the highly complicated flowfield characterized by the interaction of distinct blade associated vortical structures with the turbulent end wall boundary layer simulation results are compared with experiments and qualitative as well as quantitative agreement is observed

portfolio selection under different attitudes in fuzzy environment abstract this paper studies stock portfolio selection problem based on varying conservative neutral aggressive attitudes the return rates of stocks are characterized by fuzzy variables the pareto optimal solutions are obtained by maximizing the return and minimizing the risk subject to constraints of transaction cost and value at risk since investors with different attitudes may have different understanding of the likelihoods of occurrence measure me with the ability of reflecting varying conservative neutral aggressive attitudes is adopted based on me the expected value of fuzzy return and the lower absolute deviation are used to quantify the return and risk levels of a portfolio respectively then the constraint method is employed to obtain the efficient frontier finally an empirical study is carried out using the data of 10 stocks in chinese stock market sensitivity comparisons are conducted to demonstrate the effectiveness of the proposed model the results show that different frontiers can be obtained under different attitudes confidence levels and values at risk

homogeneity similarity based image denoising this paper presents a homogeneity similarity based method which is a new patch based image denoising method in traditional patch based methods such as the nl means method block matching mainly depends on structure similarity the homogeneity similarity is defined in adaptive weighted neighborhoods which can find more similar points than the structure similarity and so it is more effective especially for points with less repetitive patterns such as corner and end points comparative results on synthetic and real image denoising indicate that our method can effectively remove noise and preserve effective information such as edges and contrast while avoiding artifacts the application on medical image denoising also demonstrates that our method is practical

time consistent decisions and temporal decomposition of coherent risk functionals in management and planning it is commonplace for additional information to become available gradually over time it is well known that most risk measures risk functionals are time inconsistent in the following sense it may happen that at a given time period some loss distribution appears to be less risky than another one but looking at the conditional distribution at a later time the opposite relation holds almost surely the extended conditional risk functionals introduced in this paper enable a temporal decomposition of the initial risk functional that can be used to ensure consistency between past and future preferences the central result is a decomposition theorem which allows recomposing the initial coherent risk functional by compounding the conditional risk functionals without losing information or preferences it follows from our results that the revelation of partial information in time must change the decision maker s preferences for consistency reasons among the remaining courses of act

portfolio selection problem with nonlinear wealth equations under non extensive statistical mechanics for time varying sde abstract this paper is dedicated to the study of continuous time mean variance optimal portfolio selection problem with non linear wealth equations under non extensive statistical mechanics for the time varying stochastic differential equation model firstly we allow the returns and variance of risky assets are time varying functions which can fit the financial data better secondly we consider an investor with the non linear wealth equation in fact the wealth equations are not linear in many cases the investor has to pay some taxes which leads to a non linear wealth equation moreover since the return of the stocks price may be affected by a large investors portfolio selection the wealth equation is non linear in this case thirdly the non linear wealth equation driven by tsallis distribution is constructed under non extensive statistical mechanics which can capture the characteristics of fat tails and aiguilles of the risky asset s return the viscosity solution of the hjb equation for the portfolio problem is proposed by the optimal stochastic control theory and lagrange multiplier method finally the efficient portfolio strategy and efficient frontier under non extensive statistical mechanics are obtained furthermore numerical analysis and real data study are discussed to show our results

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

stability and sensitivity of optimization problems with first order stochastic dominance constraints we analyze the stability and sensitivity of stochastic optimization problems with stochastic dominance constraints of first order we consider general perturbations of the underlying probability measures in the space of regular measures equipped with a suitable discrepancy distance we show that the graph of the feasible set mapping is closed under rather general assumptions we obtain conditions for the continuity of the optimal value and upper semicontinuity of the optimal solutions as well as quantitative stability estimates of lipschitz type furthermore we analyze the sensitivity of the optimal value and obtain upper and lower bounds for the directional derivatives of the optimal value the estimates are formulated in terms of the dual utility functions associated with the dominance constraints

feature preserving mri denoising a nonparametric empirical bayes approach this paper presents a novel method for bayesian denoising of magnetic resonance mr images that bootstraps itself by inferring the prior i e the uncorrupted image statistics from the corrupted input data and the knowledge of the rician noise model the proposed method relies on principles from empirical bayes eb estimation it models the prior in a nonparametric markov random field mrf framework and estimates this prior by optimizing an information theoretic metric using the expectation maximization algorithm the generality and power of nonparametric modeling coupled with the eb approach for prior estimation avoids imposing ill fitting prior models for denoising the results demonstrate that unlike typical denoising methods the proposed method preserves most of the important features in brain mr images furthermore this paper presents a novel bayesian inference algorithm on mrfs namely iterated conditional entropy reduction icer this paper also extends the application of the proposed method for denoising diffusion weighted mr images validation results and quantitative comparisons with the state of the art in mr image denoising clearly depict the advantages of the proposed method