an efficient algorithm for the multivariable adomian polynomials abstract in this article the sum of the series of multivariable adomian polynomials is demonstrated to be identical to a rearrangement of the multivariable taylor expansion of an analytic function of the decomposition series of solutions u 1 u 2 u m about the initial solution components u 1 0 u 2 0 u m 0 of course the multivariable adomian polynomials were developed and are eminently practical for the solution of coupled nonlinear differential equations the index matrices and their simplified forms of the multivariable adomian polynomials are introduced we obtain the recurrence relations for the simplified index matrices which provide a convenient algorithm for rapid generation of the multivariable adomian polynomials another alternative algorithm for term recurrence is established in these algorithms recurrence processes do not require complicated operations such as parametrization expanding and regrouping derivatives etc as practiced in prior art the mathematica program generating the adomian polynomials based on the algorithm in this article is designed

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 reflection principle for proper holomorphic mappings of strongly pseudoconvex domains and applications this result is proved in 5 the techniques of 12 and 5 involve detailed computat ion of differential invariants on the boundary another paper philosophically related to the above but involving more elementary techniques is 1 in which proper holomorphic maps of b n to b are shown to be automorphisms more recently this result has been proved on strongly pseudoconvex domains in 2 and in 4 in the paper 3 which is the starting point for the present work completely elementary means are used to obtain a reflection principle for suitable maps of b to b k this in turn leads to a proof of the result of 12 assuming only c 2 smoothness to the boundary further detailed information is obtained about the maps even when k n 1 the elementary techniques of 3 may be adapted to use on strictly

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

a reflection principle with applications to proper holomorphic mappings j l holomorphic mappings from b into b k we then apply this principle to the problem of characterizing the proper holomorphic mappings from b into b k two such mappings f and g are said to be equivalent if there exist holomorphic automorphisms b and p of b and bk respectively such that f pogo49 there are at present three significant papers on the subject the first by alexander 1 proves that i f f is a proper holomorphic mapping of b into b then f is a holomorphic automorphism of b webster i 5 proved that for n 3 i f f is a proper holomorphic mapping of b into b 1 which is c3 then f maps b into a hyperplane in r hence using alexander s result and properties of the holomorphic automorphisms f is equivalent to the mapping zl z2 z zi z2 zn o alexander s example zl z2 z2 zlz2 z 2 shows that webster s result does not hold for n 2 in a recent paper faran 2 has characterized all proper holomorphic mappings f from b 2 to b 3 that satisfy the additional smoothness condition fec3 2 he proves that such mappings are equivalent to one of the four mappings z w z w 0 z w z zw w2 z w r z 2 l zw w2

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

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

interquad an interactive quad tree based procedure for solving the discrete alternative multiple criteria problem abstract in this paper an interactive procedure based upon a data structure called a quad tree is developed for solving the discrete alternative multiple criteria problem called interquad the procedure has been designed with large discrete alternative problems in mind interquad takes advantage of the ability of a quad tree to identify store and retrieve nondominated criterion vectors then the user interacts with the nondominated criterion vectors stored in the quad tree in a fashion similar to that of the combined tchebycheff aspiration criterion vector procedure of steuer silverman and whisman

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

a fuzzy outranking relation in multicriteria decision making abstract it frequently happens that a decision maker must establish a ranking within a finite set of alternatives with respect to multiple criteria the subjective evaluation of each alternative according to each criterion is expressed in the form of a distributive evaluation to capture the preferences of one alternative over another a concept of fuzzy outranking relation can be used this fuzzy outranking relation is characterized by a degree of credibility which is computed from two indices a confidence index and a doubt index each of these indices is calculated from the distributive evaluations over the various criteria in this paper such a fuzzy outranking relation fuzzy binary relation is constructed and an application is presented

comparison between adomian s method and he s homotopy perturbation method in this paper it is revealed that modified form of he s homotopy perturbation method corresponds to adomian s decomposition method for certain nonlinear problems

on the c version of the reflection principle for mappings between cr manifolds we prove a smooth version of the classical schwarz reflection principle for cr mappings between an abstract cr manifold m and a generic cr manifold embedded in euclidean complex space as a consequence of our results we settle a conjecture of x huang formulated in 1994

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

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

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

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

a reliable symbolic implementation of algorithm for calculating adomian polynomials in this paper we introduce a reliable symbolic implementation of the algorithm for calculating adomian polynomials and present some examples to show the simplicity and efficiency of the new method

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

uncertainty and rank order in the analytic hierarchy process abstract the analytic hierarchy process uses paired comparisons to derive a scale of relative importance for alternatives we investigate the effect of uncertainty in judgment on the stability of the rank order of alternatives the uncertainty experienced by decision makers in making comparisons is measured by associating with each judgment an interval of numerical values the approach leads to estimating the probability that an alternative or project exchanges rank with other projects these probabilities are then used to calculate the probability that project would change rank at all we combine the priority of importance of each project with the probability that it does not change rank to obtain the final ranking

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

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

a method for stochastic multiple attribute decision making based on concepts of ideal and anti ideal points this paper proposes a novel method for solving the stochastic multiple attribute decision making smadm problem where consequences of alternatives with respect to attributes are represented by random variables with cumulative distribution functions first the concepts of ideal and anti ideal cumulative distribution functions are introduced and the related theoretical analysis is given next according to the concept of classical topsis the ideal and anti ideal points of the smadm problem are determined which are in the form of cumulative distribution function vectors then the closeness coefficient of each alternative is obtained by calculating the distances to the ideal and anti ideal points simultaneously based on the obtained closeness coefficients a ranking of alternatives is determined finally two numerical examples are given to illustrate the use of the proposed method

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

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

recurrence triangle for adomian polynomials in this paper a recurrence technique for calculating adomian polynomials is proposed the convergence of the series for the adomian polynomials is discussed and the dependence of the convergent domain of the solution s decomposition series n 0 u n on the initial component function u 0 is illustrated by introducing the index vectors of the adomian polynomials the recurrence relations of the index vectors are discovered and the recurrence triangle is given the method simplifies the computation of the adomian polynomials in order to obtain a solution s decomposition series with larger domain of convergence we illustrate by examples that the domain of convergence can be changed by choosing a different u 0 and a modified iteration

an outranking method under uncertainty abstract the uncertainty of consequences and the imprecision of data often imply in multicriteria decision problems the use of probability distributions to characterize the evaluation of each action with respect to eacg criterion to keep as much information as possible the analysis should treat directly these probability distributions instead of reducing them to single values such as mean or median in this context the paper proposes a multicriteria procedure which transforms these distributive evaluations of actions according to decisionmaker s preferences in order to progress to a ranking of these actions the procedure consists for each couple of actions to construct a distributive preference degree with respect to each criterion and a distributive outranking degree over all criteria these distributive outranking degrees are then explored in order to rank the actions totally or partially

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

a method for stochastic multiple criteria decision making based on dominance degrees this paper proposes a method for solving the stochastic multiple criteria decision making smcdm problem where consequences of alternatives with respect to criteria are represented by random variables with probability distributions firstly definitions and related analysis of dominance degree of one probability distribution over another are given then by calculating the dominance degrees the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built further using promethee ii method an overall dominance degree matrix of alternative pairwise comparisons is constructed and a net flow of each alternative is calculated based on the obtained net flows a ranking of alternatives is determined finally numerical examples for the three cases are given to illustrate the use of the proposed method

on the regularity of cr mappings between cr manifolds of hypersurface type we prove smooth and analytic versions of the classical schwarz reflection principle for transversal cr mappings between two levi nondegenerate cr manifolds of hypersurface type

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

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

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

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

a method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations this paper proposes a method for solving stochastic multiple criteria decision making mcdm problems where evaluations of alternatives on considered criteria are random variables with known probability density functions or probability mass functions probabilities on all possible results of pairwise comparisons of alternatives are first calculated using probability theory then all possible results of pairwise comparisons are classified into superior indifferent and inferior ones using a predefined identification rule consequently the probabilities on all possible results of pairwise comparisons are partitioned into superior indifferent and inferior probabilities furthermore based on the derived probabilities an algorithm is developed to rank the alternatives finally a numerical example is used to illustrate the feasibility and validity of the proposed method

an alternate algorithm for computing adomian polynomials in special cases in this article we introduce an alternate algorithm for computing adomian polynomials and present some examples to show the simplicity and efficiency of the new method

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

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

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

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

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

rough approximation of a preference relation by a multi attribute stochastic dominance for determinist and stochastic evaluation problems abstract let a be a set of actions evaluated by a set of attributes two kinds of evaluations will be considered in this paper determinist or stochastic in relation to each attribute the multi attribute stochastic dominance msd r for a reduced number of attributes will be suggested to model the preferences in this kind of problem the case of mixed data where we have the attributes of different natures is not well known in the literature although it is essential from a practical point of view to apply the msd r the subset r of attributes from which approximation of the global preference is valid should be known the theory of rough sets gives us an answer on this issue allowing us to determine a minimal subset of attributes that enables the same classification of objects as the whole set of attributes in our approach these objects are pairs of actions in order to represent preferential information we shall use a pairwise comparison table this table is built for subset b a described by stochastic dominance sd relations for particular attributes and a total order for the decision attribute given by the decision maker dm using a rough set approach to the analysis of the subset of preference relations a set of decision rules is obtained and these are applied to a set a b of potential actions the rough set approach of looking for the reduction of the set of attributes gives us the possibility of operating with msd r

a new algorithm for the decomposition solution of nonlinear differential equations in this paper we introduce a new algorithm for applying the adomian decomposition method to nonlinear differential and partial differential equations the proposed algorithm does not require the explicit evaluation of adomian polynomials to approximate the nonlinearity term the numerical experiments show that the proposed algorithm is more accurate at larger values for time though at the cost of more computations

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

extending proper holomorphic mappings of positive codimension in this paper we obtain results on holomorphic continuation of proper holomorphic mappings between pseudoconvex domains with real analytic boundaries in complex spaces of different dimensions equivalently we obtain results concerning the analyticity of cauchy riemann mappings between real analytic pseudoconvex hypersurfaces in complex spaces of different dimensions to begin with we recall the corresponding results for mappings of equidimensional domains let d and d be bounded pseudoconvex domains with smooth boundaries in c if the boundaries of d and d are strictly pseudoconvex or more generally of finite type in the sense of d angelo 15 then every proper holomorphic map of d onto d extends smoothly t o according to the results of bell and catlin 7 8 and diederich and forn ess 19 for mappings between strictly pseudoconvex domains this was proved by fefferman 26 and nirenberg webster and yang 37 if the boundaries of the pseudoconvex domains d d c c are real analytic then every proper holomorphic mapping of d onto d extends holomorphically to a neighborhood of 3 according to baouendi and rothschild 2 and diederich and forn ess 21 this reflection principle was first discovered by lewy 34 and pin6uk 38 for mappings between strictly pseudoconvex domains in the case of biholomorphic mappings between weakly pseudoconvex domains with realanalytic boundaries the result follows from the work of baouendi jacobowitz and treves 5 results in this direction were obtained in recent years by several authors see the papers 4 6 18 22 33 47 49 in this paper we are treating the case when the domains d and d have different dimensions to be specific we assume that d e c and d c c n are bounded pseudoconvex domains with real analytic boundaries and n n l in this situation a proper holomorphic map f d d need not be regular at the boundary for instance there exist proper holomorphic maps of balls of different dimensions

symbolic implementation of the algorithm for calculating adomian polynomials in this paper a symbolic implementation code is developed of a technique proposed by wazwaz appl math comput 111 2000 53 for calculating adomian polynomials for nonlinear operators the algorithm proposed by him appl math comput 111 2000 53 offers a promising approach for calculating adomian polynomials for all forms of nonlinearity but it is not easy to implement due to its huge size of algebraic calculations complicated trigonometric terms and unique summation rules it is well known that the algebraic manipulation language such as mathematica is useful to facilitate such a hard computational work pattern matching capabilities peculiar feature of mathematica are used in index regrouping which is a key role in constructing adomian polynomials the computer algebra software mathematica is used to collect terms to their order and to simplify the terms the symbolic implementation code author developed appearing at appendix has the flexibility that may easily cover any length of adomian polynomial for many forms of nonlinear cases a nonlinear evolution equation is investigated in order to justify the availability of symbolic implementation code

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

convenient analytic recurrence algorithms for the adomian polynomials abstract in this article we present four analytic recurrence algorithms for the multivariable adomian polynomials as special cases we deduce the four simplified results for the one variable adomian polynomials these algorithms are comprised of simple orderly and analytic recurrence formulas which do not require time intensive operations such as expanding regrouping parametrization and so on they are straightforward to implement in any symbolic software and are shown to be very efficient by our verification using mathematica 7 0 we emphasize that from the summation expressions a n k 1 n u n k for the multivariable adomian polynomials and an k 1 n f k u 0 c n k for the one variable adomian polynomials we obtain the recurrence formulas for the u n k and the c n k these provide a theoretical basis for developing new algorithmic approaches such as for parallel computing in particular the recurrence process of one particular algorithm for the one variable adomian polynomials does not involve the differentiation operation but significantly only the arithmetic operations of multiplication and addition are involved precisely c n 1 u n n 1 and c n k 1 n j 0 n k j 1 u j 1 c n 1 j k 1 2 k n we also discuss several other algorithms previously reported in the literature including the adomian rach recurrence algorithm 1 and this author s index recurrence algorithm 23 36