computational methods for risk averse undiscounted transient markov models the total cost problem for discrete time controlled transient markov models is considered the objective functional is a markov dynamic risk measure of the total cost two solution methods value and policy iteration are proposed and their convergence is analyzed in the policy iteration method we propose two algorithms for policy evaluation the nonsmooth newton method and convex programming and we prove their convergence the results are illustrated on a credit limit control problem

theoretical and semantic distinctions of fuzzy possibilistic and mixed fuzzy possibilistic optimization theoretical semantic and algorithmic distinctions among fuzzy possibilistic and mixed fuzzy possibilistic optimization are presented and illustrated the theory underlying fuzzy possibilistic and mixed fuzzy possibilistic optimization is developed and demonstrated and points to the appropriate use of distinct solution methods associated with each type of optimization dependant on the semantics of the problem semantics is key to both the input where one is obtaining the data and constructing the optimization model in the presence of uncertainty and the output where the meaning of the results is necessary for understanding solutions the case in which the optimization model arises from the data that is a combination of fuzzy and possibilistic distributions is also derived lastly examples illustrate the theory this paper is a modification and an amplification of a presentation made at ifsa 05 w a lodwich k d jamison theory and semantics for fuzzy and possibilistic optimization in fuzzy logic soft computing and computational intelligence eleventh internat fuzzy systems association world congress july 28 31 2005 beijing china vol iii pp 1805 1810 26

portfolio optimization problem under concave transaction costs and minimal transaction unit constraints we will propose a branch and bound algorithm for calculating a globally optimal solution of a portfolio construction rebalancing problem under concave transaction costs and minimal transaction unit constraints we will employ the absolute deviation of the rate of return of the portfolio as the measure of risk and solve linear programming subproblems by introducing piecewise linear underestimating function for concave transaction cost functions it will be shown by a series of numerical experiments that the algorithm can solve the problem of practical size in an efficient manner

valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints stochastic dominance relations are well studied in statistics decision theory and economics recently there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints in the discrete case stochastic optimization models involving second order stochastic dominance constraints can be solved by linear programming however problems involving first order stochastic dominance constraints are potentially hard due to the non convexity of the associated feasible regions in this paper we consider a mixed 0 1 linear programming formulation of a discrete first order constrained optimization model and present a relaxation based on second order constraints we derive some valid inequalities and restrictions by employing the probabilistic structure of the problem we also generate cuts that are valid inequalities for the disjunctive relaxations arising from the underlying combinatorial structure of the problem by applying the lift and project procedure we describe three heuristic algorithms to construct feasible solutions based on conditional second order constraints variable fixing and conditional value at risk finally we present numerical results for several instances of a real world portfolio optimization problem

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

a multiproduct risk averse newsvendor with law invariant coherent measures of risk we consider a multiproduct risk averse newsvendor under the law invariant coherent measures of risk we first establish several fundamental properties of the model regarding the convexity of the problem the symmetry of the solution and the impact of risk aversion specifically we show that for identical products with independent demands increased risk aversion leads to decreased orders for a large but finite number of heterogeneous products with independent demands we derive closed form approximations for the optimal order quantities the approximations are as simple to compute as the classical risk neutral solutions we also show that the risk neutral solution is asymptotically optimal as the number of products tends to be infinity and thus risk aversion has no impact in the limit for a risk averse newsvendor with dependent demands we show that positively negatively dependent demands lead to lower higher optimal order quantities than independent demands using a numerical study we examine the convergence rates of the approximations and develop additional insights into the interplay between dependent demands and risk aversion

orlicz spaces equipped with s norms abstract on orlicz spaces of measurable functions the classical orlicz and luxemburg norm can be defined by use of the amemiya formula x o inf k 0 1 k 1 i k x and x inf k 0 1 k max 1 i k x respectively where is an orlicz function and i x t x t d t based on this observation in the last few years a number of papers have been published that dealt with the geometrical properties of orlicz spaces equipped with the so called p amemiya norms defined by x p inf k 0 1 k 1 i p k x 1 p where 1 p the aim of this paper is to present a general and universal method of introducing norms in orlicz spaces that will cover all the cases mentioned above namely using the concept of outer function s norms x s inf k 0 1 k s i k x are introduced it is proved that to each outer function s we can associate an outer function s that is conjugate to s in the holder sense i e u v s u s v for all u v 0 moreover it is proved under some minor assumptions that the kothe dual of the subspace e of the orlicz space equipped with the s norm s is an orlicz space l equipped with the s norm s where the outer function s is conjugate to s in the holder sense and the orlicz function is complementary to in the young sense

stochastic programming approach to optimization under uncertainty in this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems we argue that two stage say linear stochastic programming problems can be solved with a reasonable accuracy by monte carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages we discuss an extension of coherent risk measures to a multistage setting and in particular dynamic programming equations for such problems

twenty years of linear programming based portfolio optimization markowitz formulated the portfolio optimization problem through two criteria the expected return and the risk as a measure of the variability of the return the classical markowitz model uses the variance as the risk measure and is a quadratic programming problem many attempts have been made to linearize the portfolio optimization problem several different risk measures have been proposed which are computationally attractive as for discrete random variables they give rise to linear programming lp problems about twenty years ago the mean absolute deviation mad model drew a lot of attention resulting in much research and speeding up development of other lp models further the lp models based on the conditional value at risk cvar have a great impact on new developments in portfolio optimization during the first decade of the 21st century the lp solvability may become relevant for real life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved in this paper we review the variety of lp solvable portfolio optimization models presented in the literature the real features that have been modeled and the solution approaches to the resulting models in most of the cases mixed integer linear programming milp models we also discuss the impact of the inclusion of the real features

third degree stochastic dominance and mean risk analysis in their recent article ogryczak and ruszczynski 1999 proved that those portfolios associated with the efficient frontiers generated by mean lower semi standard deviation model and mean lower semi absolute deviation model are efficient in the sense of second degree stochastic dominance this rather surprising result reveals the importance of lower partial risk models in portfolio analysis in this paper we extend the results of ogryczak and ruszczynski for second degree stochastic dominance to third degree stochastic dominance we show that portfolios on a significant portion of the efficient frontier generated by mean lower semi skewness model are efficient in the sense of third degree stochastic dominance also we prove that the portfolios generated by mean variance skewness model are semi efficient in the sense of third degree stochastic dominance

multilevel image coding with hyperfeatures histograms of local appearance descriptors are a popular representation for visual recognition they are highly discriminant with good resistance to local occlusions and to geometric and photometric variations but they are not able to exploit spatial co occurrence statistics over scales larger than the local input patches we present a multilevel visual representation that remedies this the starting point is the notion that to detect object parts in images in practice it often suffices to detect co occurrences of more local object fragments this can be formalized by coding image patches against a codebook of known fragments or a more general statistical model and locally histogramming the resulting labels to capture their co occurrence statistics local patch descriptors are converted into somewhat less local histograms over label occurrences the histograms are themselves local descriptor vectors so the process can be iterated to code ever larger assemblies of object parts and increasingly abstract or semantic image properties we call these higher level descriptors hyperfeatures we formulate the hyperfeature model and study its performance under several different image coding methods including k means based vector quantization gaussian mixtures and combinations of these with latent dirichlet allocation we find that the resulting high level features provide improved performance in several object image and texture image classification tasks

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

risk optimization with p order conic constraints a linear programming approach the paper considers solving of linear programming problems with p order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints the proposed approach is based on construction of polyhedral approximations for p order cones and then invoking a benders decomposition scheme that allows for efficient solving of the approximating problems the conducted case study of portfolio optimization with p order conic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods including second order conic programming methods

robust stochastic dominance and its application to risk averse optimization we introduce a new preference relation in the space of random variables which we call robust stochastic dominance we consider stochastic optimization problems where risk aversion is expressed by a robust stochastic dominance constraint these are composite semi infinite optimization problems with constraints on compositions of measures of risk and utility functions we develop necessary and sufficient conditions of optimality for such optimization problems in the convex case in the nonconvex case we derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

worst case robust omega ratio abstract the omega ratio is a recent performance measure proposed to overcome the known shortcomings of the sharpe ratio until recently the omega ratio was thought to be computationally intractable and research was focused on heuristic optimization procedures we have shown elsewhere that the omega ratio optimization is equivalent to a linear program and hence can be solved exactly in polynomial time this permits the investigation of more complex and realistic variants of the problem the standard formulation of the omega ratio requires perfect information for the probability distribution of the asset returns in this paper we investigate the problem arising from the probability distribution of the asset returns being only partially known we introduce the robust variant of the conventional omega ratio that hedges against uncertainty in the probability distribution we examine the worst case omega ratio optimization problem under three types of uncertainty mixture distribution box and ellipsoidal uncertainty and show that the problem remains tractable

efficient and effective visual codebook generation using additive kernels common visual codebook generation methods used in a bag of visual words model for example k means or gaussian mixture model use the euclidean distance to cluster features into visual code words however most popular visual descriptors are histograms of image measurements it has been shown that with histogram features the histogram intersection kernel hik is more effective than the euclidean distance in supervised learning tasks in this paper we demonstrate that hik can be used in an unsupervised manner to significantly improve the generation of visual codebooks we propose a histogram kernel k means algorithm which is easy to implement and runs almost as fast as the standard k means the hik codebooks have consistently higher recognition accuracy over k means codebooks by 2 4 in several benchmark object and scene recognition data sets the algorithm is also generalized to arbitrary additive kernels its speed is thousands of times faster than a naive implementation of the kernel k means algorithm in addition we propose a one class svm formulation to create more effective visual code words finally we show that the standard k median clustering method can be used for visual codebook generation and can act as a compromise between the hik additive kernel and the k means approaches

optimization with multivariate stochastic dominance constraints we consider stochastic optimization problems where risk aversion is expressed by a stochastic ordering constraint the constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector we identify a suitable multivariate stochastic order and describe its generator in terms of von neumann morgenstern utility functions we develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint assuming convexity we show that the lagrange multipliers corresponding to dominance constraints are elements of the generator of this order thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints furthermore we obtain necessary conditions of optimality for non convex problems under additional smoothness assumptions

insdecm an interactive procedure for stochastic multicriteria decision problems abstract a new interactive technique for a discrete stochastic multiattribute decision making problem is proposed in this paper it is assumed that performance probability distribution for each action on each attribute is known two concepts are combined in the procedure stochastic dominance and interactive approach the first one is employed for generating efficient actions and constructing rankings of actions with respect to attributes the second concept is used when the communication between the dm and the model is conducted it is assumed that decision maker s restrictions are defined by specifying minimal or maximal values of scalar criteria measuring either expected outcome or variability of outcomes as such restrictions are in general not consistent with stochastic dominance rules we suggest verifying this consistency and asking the decision maker to redefine inconsistent restrictions

conditional risk mappings we introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties in particular we prove a representation theorem for conditional risk mappings in terms of conditional expectations we also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings

conditional value at risk in stochastic programs with mixed integer recourse in classical two stage stochastic programming the expected value of the total costs is minimized recently mean risk models studied in mathematical finance for several decades have attracted attention in stochastic programming we consider conditional value at risk as risk measure in the framework of two stage stochastic integer programming the paper addresses structure stability and algorithms for this class of models in particular we study continuity properties of the objective function both with respect to the first stage decisions and the integrating probability measure further we present an explicit mixed integer linear programming formulation of the problem when the probability distribution is discrete and finite finally a solution algorithm based on lagrangean relaxation of nonanticipativity is proposed

polyhedral risk measures in stochastic programming we consider stochastic programs with risk measures in the objective and study stability properties as well as decomposition structures thereby we place emphasis on dynamic models i e multistage stochastic programs with multiperiod risk measures in this context we define the class of polyhedral risk measures such that stochastic programs with risk measures taken from this class have favorable properties polyhedral risk measures are defined as optimal values of certain linear stochastic programs where the arguments of the risk measure appear on the right hand side of the dynamic constraints dual representations for polyhedral risk measures are derived and used to deduce criteria for convexity and coherence as examples of polyhedral risk measures we propose multiperiod extensions of the conditional value at risk

numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization inspired by the successful applications of the stochastic optimization with second order stochastic dominance ssd model in portfolio optimization we study new numerical methods for a general ssd model where the underlying functions are not necessarily linear specifically we penalize the ssd constraints to the objective under slater s constraint qualification and then apply the well known stochastic approximation sa method and the level function method to solve the penalized problem both methods are iterative the former requires to calculate an approximate subgradient of the objective function of the penalized problem at each iterate while the latter requires to calculate a subgradient under some moderate conditions we show that w p 1 the sequence of approximated solutions generated by the sa method converges to an optimal solution of the true problem as for the level function method the convergence is deterministic and in some cases we are able to estimate the number of iterations for a given precision both methods are applied to portfolio optimization problem where the return functions are not necessarily linear and some numerical test results are reported

frontiers of stochastically nondominated portfolios we consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution we propose mean risk models that are solvable by linear programming and generate portfolios whose returns are nondomi nated in the sense of second order stochastic dominance next we develop a specialized parametric method for recovering the entire mean risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and real izations the problem of optimizing a portfolio of finitely many assets is a classical problem in theoretical and computational finance since the seminal work of markowitz 1952 it is generally agreed that portfolio performance should be measured in two distinct dimen sions the mean describing the expected return and the risk which measures the uncer tainty of the return in the mean risk approach we select from the universe of all possible portfolios those that are efficient for a given value of the mean they minimize the risk or equivalently for a given value of risk they maximize the mean such an approach has many advantages it allows one to formulate the problem as a parametric optimization problem and it facilitates the trade off analysis between mean and risk markowitz used the variance of the return as the measure of the risk it is easy to compute and it reduces the portfolio selection problem to a parametric quadratic pro gramming problem one can however construct simple counterexamples that show the imperfection of the variance as the risk measure it treats over performance equally as under performance and more importantly its use may suggest a portfolio that is always outperformed by another portfolio the use of the semivariance rather than the variance was already recommended by markowitz 1959 but even in this case significant deficien cies remain as we shall explain another theoretical approach to the portfolio selection problem is that of stochastic dominance see whitmore and findlay 1978 levy 1992 the usual first order defi nition of stochastic dominance gives a partial order in the space of real random variables more important from the portfolio point of view is the notion of second order dominance which is also defined as a partial order but which is equivalent to this statement a random variable y dominates the random variable z if e u y e u z for all nondecreasing concave functions u for which these expected values are finite thus no risk averse decision marker will prefer a portfolio with return z over a portfolio with return y while

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

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

discrete dynamic programming with outcomes in random variable structures abstract multiobjective approach is the common way of generalization single criterion dynamic programming models another way is to consider partially ordered criteria structures that approach is rather rare the aim of the paper is to present such a model generalization of bellman s principle of optimality is employed to create a forward procedure to find the set of all maximal elements as this set is usual large the second problem under consideration is to find its subsets to reduce the number of solutions presented to decision maker we propose to apply a family of narrowing relations that approach is similar to scalarization in multiobjective programming ordered structures of random variables based on mean variance stochastic dominance and inverse stochastic dominance are considered numerical illustration is given at the end of the paper

risk forms representation disintegration and application to partially observable two stage systems we introduce the concept of a risk form which is a real functional of two arguments a measurable function on a polish space and a measure on that space we generalize the duality theory and the kusuoka representation to this setting for a risk form acting on a product of polish spaces we define marginal and conditional forms and we prove a disintegration formula which represents a risk form as a composition of its marginal and conditional forms we apply the proposed approach to two stage stochastic programming problems with partial information and decision dependent observation distribution

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

aspiration level approach in stochastic mcdm problems the paper considers a discrete stochastic multiple criteria decision making problem this problem is defined by a finite set of actions a a set of attributes x and a set of evaluations of actions with respect to attributes e in stochastic case the evaluation of each action with respect to each attribute takes form of a probability distribution thus the comparison of two actions leads to the comparison of two vectors of probability distributions in the paper a new procedure for solving this problem is proposed it is based on three concepts stochastic dominance interactive approach and preference threshold the idea of the procedure comes from the interactive multiple objective goal programming approach the set of actions is progressively reduced as the decision maker specifies additional requirements at the beginning the decision maker is asked to define preference threshold for each attribute next at each iteration the decision maker is confronted with the set of considered actions if the decision maker is able to make a final choice then the procedure ends otherwise he she is asked to specify aspiration level a didactical example is presented to illustrate the proposed technique

weakly supervised learning of visual models and its application to content based retrieval this paper presents a method for weakly supervised learning of visual models the visual model is based on a two layer image description a set of generic descriptors and their distribution over neighbourhoods generic descriptors represent sets of similar rotational invariant feature vectors statistical spatial constraints describe the neighborhood structure and make our description more discriminant the joint probability of the frequencies of generic descriptors over a neighbourhood is multi modal and is represented by a set of neighbourhood frequency clusters our image description is rotationally invariant robust to model deformations and characterizes efficiently appearance based visual structure the selection of distinctive clusters determines model features common to the positive and rare in the negative examples visual models are retrieved and localized using a probabilistic score experimental results for textured animals and faces show a very good performance for retrieval as well as localization

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

exact penalization level function method and modified cutting plane method for stochastic programs with second order stochastic dominance constraints level function methods and cutting plane methods have been recently proposed to solve stochastic programs with stochastic second order dominance ssd constraints a level function method requires an exact penalization setup because it can only be applied to the objective function not the constraints slater constraint qualification scq is often needed for deriving exact penalization it is well known that ssd usually does not satisfy scq and various relaxation schemes have been proposed so that the relaxed problem satisfies the scq in this paper we show that under some moderate conditions the desired constraint qualification can be guaranteed through some appropriate reformulation of the constraints rather than relaxation exact penalization schemes based on l 1 norm and l infty norm are subsequently derived through robinson s error bound on convex systems and clarke s exact penalty function theorem moreover we propose a modified cutting plane method which constructs a cutting plane through t

optimization with stochastic dominance constraints we introduce stochastic optimization problems involving stochastic dominance constraints we develop necessary and sufficient conditions of optimality and duality theory for these models and show that the lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions the models and results are illustrated on a portfolio optimization problem

mining mid level features for image classification mid level or semi local features learnt using class level information are potentially more distinctive than the traditional low level local features constructed in a purely bottom up fashion at the same time they preserve some of the robustness properties with respect to occlusions and image clutter in this paper we propose a new and effective scheme for extracting mid level features for image classification based on relevant pattern mining in particular we mine relevant patterns of local compositions of densely sampled low level features we refer to the new set of obtained patterns as frequent local histograms or flhs during this process we pay special attention to keeping all the local histogram information and to selecting the most relevant reduced set of flh patterns for classification the careful choice of the visual primitives and an extension to exploit both local and global spatial information allow us to build powerful bag of flh based image representations we show that these bag of flhs are more discriminative than traditional bag of words and yield state of the art results on various image classification benchmarks including pascal voc

random variables monotone relations and convex analysis random variables can be described by their cumulative distribution functions a class of nondecreasing functions on the real line those functions can in turn be identified after the possible vertical gaps in their graphs are filled in with maximal monotone relations such relations are known to be the subdifferentials of convex functions analysis of these connections yields new insights the generalized inversion operation between distribution functions and quantile functions corresponds to graphical inversion of monotone relations in subdifferential terms it corresponds to passing to conjugate convex functions under the legendre fenchel transform among other things this shows that convergence in distribution for sequences of random variables is equivalent to graphical convergence of the monotone relations and epigraphical convergence of the associated convex functions measures of risk that employ quantiles var and superquantiles cvar either individually or in mixtures are illuminated in this way formulas for their calculation are seen from a perspective that reveals how they were discovered the approach leads further to developments in which the superquantiles for a given distribution are interpreted as the quantiles for an overlying superdistribution in this way a generalization of koenker basset error is derived which lays a foundation for superquantile regression as a higher order extension of quantile regression

risk averse two stage stochastic linear programming modeling and decomposition we formulate a risk averse two stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage the objective function is formulated as a composition of conditional risk measures we analyze properties of the problem and derive necessary and sufficient optimality conditions next we construct a new decomposition method for solving the problem that exploits the composite structure of the objective function we illustrate its performance on a portfolio optimization problem

two level schwarz methods for the biharmonic problem discretized by conforming c 1 elements additive schwarz methods are overlapping domain decomposition methods proposed by dryja and widlund for second order elliptic problems in this paper we consider two level additive schwarz methods for the biharmonic dirichlet problem discretized by conforming c 1 finite elements most of these elements are nonnested in the sense that the finite element space defined on the coarse mesh is not a subspace of the space defined on the finer mesh we construct certain intergrid transfer operators and establish that the algorithms have optimal convergence properties our algorithms include the cases when the two level triangulation are nonnested and the subspaces on the coarse and the fine grids are defined by different finite elements our analysis is based on the theory of dryja and widlund and our estimates use the stable approximation properties of the finite elements and the intergrid transfer operators

recognition without correspondence using multidimensionalreceptive field histograms the appearance of an object is composed of local structure this local structure can be described and characterized by a vector of local features measured by local operators such as gaussian derivatives or gabor filters this article presents a technique where appearances of objects are represented by the joint statistics of such local neighborhood operators as such this represents a new class of appearance based techniques for computer vision based on joint statistics the paper develops techniques for the identification of multiple objects at arbitrary positions and orientations in a cluttered scene experiments show that these techniques can identify over 100 objects in the presence of major occlusions most remarkably the techniques have low complexity and therefore run in real time

a modified particle swarm optimization algorithm with applications abstract in this paper firstly a modified particle swarm optimization algorithm mpso is developed in which the mean value of past optimal positions for each particle and the mutation operation are considered for avoiding premature in the optimization test mpso performs better than particle swarm optimization algorithm pso then mpso is applied to solve four portfolio optimization models with the real data from the hong kong stock market and optimal values are obtained when the number of swarm n 80 160 respectively finally actual return rates of these models are calculated in numerical experiments and it is illustrated from these graphs of actual return rates that when considering higher return cai s model performs better in short term investment

artificial bee colony algorithm for constrained possibilistic portfolio optimization problem abstract in this paper we discuss the portfolio optimization problem with real world constraints under the assumption that the returns of risky assets are fuzzy numbers a new possibilistic mean semiabsolute deviation model is proposed in which transaction costs cardinality and quantity constraints are considered due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently thus a modified artificial bee colony mabc algorithm is developed to solve the corresponding optimization problem finally a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm

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

process based risk measures and risk averse control of discrete time systems for controlled discrete time stochastic processes we introduce a new class of dynamic risk measures which we call process based their main feature is that they measure risk of processes that are functions of the history of a base process we introduce a new concept of conditional stochastic time consistency and we derive the structure of process based risk measures enjoying this property we show that they can be equivalently represented by a collection of static law invariant risk measures on the space of functions of the state of the base process we apply this result to controlled markov processes and we derive dynamic programming equations we also derive dynamic programming equations for multistage stochastic programming with decision dependent distributions

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

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

additive consistency of risk measures and its application to risk averse routing in networks we investigate the use of risk measures and theories of choice to model risk averse routing and traffic equilibrium on networks with random travel times we interpret the postulates of these theories in the context of routing identifying additive consistency as a plausible condition that allows to reduce risk averse route choice to a standard shortest path problem within the classical theories of choice we show that the only preferences that satisfy this condition are the ones induced by the entropic risk measures

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

risk adjusted probability measures in portfolio optimization with coherent measures of risk abstract we consider the problem of optimizing a portfolio of n assets whose returns are described by a joint discrete distribution we formulate the mean risk model using as risk functionals the semideviation deviation from quantile and spectral risk measures using the modern theory of measures of risk we derive an equivalent representation of the portfolio problem as a zero sum matrix game and we provide ways to solve it by convex optimization techniques in this way we reconstruct new probability measures which constitute part of the saddle point of the game these risk adjusted measures always exist irrespective of the completeness of the market we provide an illustrative example in which we derive these measures in a universe of 200 assets and we use them to evaluate the market portfolio and optimal risk averse portfolios

portfolio construction based on stochastic dominance and target return distributions mean risk models have been widely used in portfolio optimization however such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk averse investors this paper considers the problem of constructing a portfolio which is non dominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties the problem is multi objective and is transformed into a single objective problem by using the reference point method in which target levels known as aspiration points are specified for the objective functions a model is proposed in which the aspiration points relate to ordered outcomes for the portfolio return this concept is extended by additionally specifying reservation points which act pre emptively in the optimization model the theoretical properties of the models are studied the performance of the models on real data drawn from the hang seng index is also investigated

kernel search an application to the index tracking problem abstract in this paper we study the problem of replicating the performances of a stock market index i e the so called index tracking problem and the problem of out performing a market index i e the so called enhanced index tracking problem we introduce mixed integer linear programming milp formulations for these two problems furthermore we present a heuristic framework called kernel search we analyze and evaluate the behavior of several implementations of the kernel search framework to the solution of the index tracking problem we show the effectiveness and efficiency of the framework comparing the performances of these heuristics with those of a general purpose solver the computational experiments are carried out using benchmark and newly created instances

linear programming models based on omega ratio for the enhanced index tracking problem abstract modern performance measures differ from the classical ones since they assess the performance against a benchmark and usually account for asymmetry in return distributions the omega ratio is one of these measures until recently limited research has addressed the optimization of the omega ratio since it has been thought to be computationally intractable the enhanced index tracking problem eitp is the problem of selecting a portfolio of securities able to outperform a market index while bearing a limited additional risk in this paper we propose two novel mathematical formulations for the eitp based on the omega ratio the first formulation applies a standard definition of the omega ratio where it is computed with respect to a given value whereas the second formulation considers the omega ratio with respect to a random target we show how each formulation nonlinear in nature can be transformed into a linear programming model we further extend the models to include real features such as a cardinality constraint and buy in thresholds on the investments obtaining mixed integer linear programming problems computational results conducted on a large set of benchmark instances show that the portfolios selected by the model assuming a standard definition of the omega ratio are consistently outperformed in terms of out of sample performance by those obtained solving the model that considers a random target furthermore in most of the instances the portfolios optimized with the latter model mimic very closely the behavior of the benchmark over the out of sample period while yielding sometimes significantly larger returns

risk aversion via excess probabilities in stochastic programs with mixed integer recourse we consider linear two stage stochastic programs with mixed integer recourse instead of basing the selection of an optimal first stage solution on expected costs alone we include into the objective a risk term reflecting the probability that a preselected cost threshold is exceeded after we have put the resulting mean risk model into perspective with stochastic dominance we study further structural properties of the model and derive some basic stability results in the algorithmic part of the paper we propose a scenario decomposition method and report initial computational experience

risk averse dynamic programming for markov decision processes we introduce the concept of a markov risk measure and we use it to formulate risk averse control problems for two markov decision models a finite horizon model and a discounted infinite horizon model for both models we derive risk averse dynamic programming equations and a value iteration method for the infinite horizon problem we develop a risk averse policy iteration method and we prove its convergence we also propose a version of the newton method to solve a nonsmooth equation arising in the policy iteration method and we prove its global convergence finally we discuss relations to min max markov decision models