an algorithm for portfolio selection in a frictional market absolute deviation is utilized as a measure of risk and a new function is provided for it we consider the mean absolute deviation mad portfolio optimization problem in a frictional market with additional constraints representing the so called short sales an algorithm for solving the optimization problem is thus presented which uses the special structure of the original problem to reduce to a linear programming the numerical test shows the validity of the method

on the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes let x t be a diffusion process on r d with generator l 1 2 nabla cdot a nabla b nabla and let p x x in r d be the corresponding measures on paths pick 0 s which are always satisfied if a 1 b is a gradient function we show that y t s is an inhomogeneous diffusion process and that as t rightarrow infty y t s 0 leq s leq t converges to a limiting homogeneous positive recurrent diffusion y s 0 leq s leq t with state space g since t is arbitrary we actually obtain a limiting process y s 0 leq s infty the generator of the limiting process may be written in the form l g 1 2 nabla cdot a nabla b nabla a nabla g 0 g 0 nabla a nabla h g 0 nabla where g 0 is the square root of the density of a measure mu 0 which minimizes the i function for the process over all gamma in mathscr p bar g the set of probability measures on bar g the function h g 0 appears in the explicit calculation of i mu 0 and solves a certain variational equation the invariant measure for the process is mu 0

a martingale approach to metastability we presented in beltran and landim j stat phys 140 1065 1114 2010 beltran and landim j stat phys 149 598 618 2012 an approach to derive the metastable behavior of continuous time markov chains we assumed in these articles that the markov chains visit points in the time scale in which it jumps among the metastable sets we replace this condition here by assumptions on the mixing times and on the relaxation times of the chains reflected at the boundary of the metastable sets

a novel multi period mean var portfolio optimization model considering practical constraints and transaction cost abstract the portfolio optimization literature has spent a little effort to consider the fat tail characteristic of asset returns as well as their extreme events to remove such shortcomings in this paper a novel portfolio optimization model is developed in which value at risk var is utilized as a risk measure to account extreme risk so that var is estimated use of extreme value theory evt to enrich the practicality of our proposed model set of real trading constraints are considered such as cardinality budget floor and ceiling constraints since these modifications lead to a non convex np hard problem which is computationally difficult a new design of non dominated sorting genetic algorithm nsga ii is proposed to solve it to evaluate the performance of evt approach in our proposed mean var model three well known alternative var estimation methods are also considered such as historical simulation garch and t student garch experimental results using historical daily financial market data from s p 100 indices demonstrates that our proposed nsga ii has great capability of treating the mean var portfolio optimization problem in addition the validation study confirmed that our enhanced nsga ii not only offers superior result compared with that of delivered by benchmark problem in a much lower solving time but its performance is better than the original nsga ii also the results indicate that our proposed model outperforms other mean var models especially in low risk area of pareto front finally the proposed algorithm is compared with set of non dominated based algorithms including spea ii nspso and nsaco which results illustrated that our enhanced nsga ii suggests superior solutions rather than other algorithms

on the existence of solutions to the quadratic mixed integer mean variance portfolio selection problem abstract in the standard mean variance portfolio selection approach several operative features are not taken into account among these neglected aspects one of particular interest is the finite divisibility of the stock assets i e the obligation to buy sell only integer quantities of asset lots whose number is pre established in order to consider such a feature we deal with a suitably defined quadratic mixed integer programming problem in particular we formulate this problem in terms of quantities of asset lots instead of as usual in terms of capital per cent quotas secondly we provide necessary and sufficient conditions for the existence of a non empty mixed integer feasible set of the considered programming problem thirdly we present some rounding procedures for finding in a finite number of steps a feasible mixed integer solution which is better than the one detected by the necessary and sufficient conditions in terms of the value assumed by the portfolio variance finally we perform an extensive computational experiment by means of which we verify the goodness of our approach

multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints abstract this paper considers a multiperiod fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control in which the returns of assets are characterized by possibilistic mean values a possibilistic absolute deviation is defined as the risk control of portfolio a new multiperiod mean absolute deviation fuzzy portfolio selection model with transaction cost borrowing constraints threshold constraints and cardinality constraints is proposed based on the theory of possibility measure the proposed model is transformed into a crisp nonlinear programming problem because of the transaction cost the multiperiod portfolio selection is a dynamic optimization problem with path dependence the discrete approximate iteration method is designed to obtain the optimal portfolio strategy and is proved convergent finally an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the shanghai stock exchange

recurrence of random walk traces we show that the edges crossed by a random walk in a network form a recurrent graph a s in fact the same is true when those edges are weighted by the number of crossings

decomposition algorithms for two stage chance constrained programs we study a class of chance constrained two stage stochastic optimization problems where second stage feasible recourse decisions incur additional cost in addition we propose a new model where recovery decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second stage problem we develop decomposition algorithms with specialized optimality and feasibility cuts to solve this class of problems computational results on a chance constrained resource planing problem indicate that our algorithms are highly effective in solving these problems compared to a mixed integer programming reformulation and a naive decomposition method

covariance analysis in siso linear systems identification in this paper we analyze the asymptotic covariance of models of causal single input single output linear time invariant systems expressions for the asymptotic co variance of system properties es

hitting times of rare events in markov chains a general condition for a markov process with finite states is given for the convergence of the normalized hitting time of a rare event to a mean one exponential law it is then applied to the boundary driven symmetric simple exclusion process for an open set of density profiles which does not contain the stationary density profile

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

convexity and decomposition of mean risk stochastic programs traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criterion a common approach to addressing risk in decision making problems is to consider a weighted mean risk objective where some dispersion statistic is used as a measure of risk we investigate the computational suitability of various mean risk objective functions in addressing risk in stochastic programming models we prove that the classical mean variance criterion leads to computational intractability even in the simplest stochastic programs on the other hand a number of alternative mean risk functions are shown to be computationally tractable using slight variants of existing stochastic programming decomposition algorithms we propose decomposition based parametric cutting plane algorithms to generate mean risk efficient frontiers for two particular classes of mean risk objectives

guaranteed characterization of exact non asymptotic confidence regions as defined by lscr and sps in parameter estimation it is often desirable to supplement the estimates with an assessment of their quality a new family of methods proposed by campi et al for this purpose is particularly attractive as it makes it possible to obtain exact non asymptotic confidence regions under mild assumptions on the noise distribution a bottleneck of this approach however is the numerical characterization of these confidence regions so far it has been carried out by gridding which provides no guarantee as to its results and is only applicable to low dimensional spaces this paper shows how interval analysis can contribute to removing this bottleneck

stochastic programming with integer variables including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design starting from mean risk approaches with different risk measures we identify corresponding two and multi stage stochastic integer programs that are large scale block structured mixed integer linear programs if the underlying probability distributions are discrete we highlight the role of mixed integer value functions for structure and stability of stochastic integer programs when applied to the block structures in stochastic integer programming well known algorithmic principles such as branch and bound lagrangian relaxation or cutting plane methods open up new directions of research we review existing results in the field and indicate departure points for their extension

portfolios with fuzzy returns selection strategies based on semi infinite programming this paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables the investor s problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset the corresponding optimal portfolio is derived using semi infinite programming in a soft framework the return on each asset and their membership functions are described using historical data the investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio this approach is illustrated with a numerical example

on solving discrete two stage stochastic programs having mixed integer first and second stage variables in this paper we propose a decomposition based branch and bound dbab algorithm for solving two stage stochastic programs having mixed integer first and second stage variables a modified benders decomposition method is developed where the benders subproblems define lower bounding second stage value functions of the first stage variables that are derived by constructing a certain partial convex hull representation of the two stage solution space this partial convex hull is sequentially generated using a convexification scheme such as the reformulation linearization technique rlt or lift and project process which yields valid inequalities that are reusable in the subsequent subproblems by updating the values of the first stage variables a branch and bound algorithm is designed based on a hyperrectangular partitioning process using the established property that any resulting lower bounding benders master problem defined over a hyperrectangle yields the same objective value as the original stochastic program over that region if the first stage variable solution is an extreme point of the defining hyperrectangle or the second stage solution satisfies the binary restrictions we prove that this algorithm converges to a global optimal solution some numerical examples and computational results are presented to demonstrate the efficacy of this approach

duality and martingales a stochastic programming perspective on contingent claims the hedging of contingent claims in the discrete time discrete state case is analyzed from the perspective of modeling the hedging problem as a stochastic program application of conjugate duality leads to the arbitrage pricing theorems of financial mathematics namely the equivalence of absence of arbitrage and the existence of a probability measure that makes the price process into a martingale the model easily extends to the analysis of options pricing when modeling risk management concerns and the impact of spreads and margin requirements for writers of contingent claims however we find that arbitrage pricing in incomplete markets fails to model incentives to buy or sell options an extension of the model to incorporate pre existing liabilities and endowments reveals the reasons why buyers and sellers trade in options the model also indicates the importance of financial equilibrium analysis for the understanding of options prices in incomplete markets

on evaluating the donsker varadhan i function let x t be a feller process on a complete separable metric space a and consider the occupation measure l t omega cdot int t 0 chi cdot x s ds the i function is defined for mu in mathscr p a the set of probability measures on a by i mu inf u in mathscr d int a lu u d mu where l mathscr d is the generator of the process and mathscr d subset mathscr d consists of the strictly positive functions in mathscr d the i function determines the asymptotic rate of decay of p 1 t l t omega cdot in g for g subset mathscr p a the first difficulty encountered in evaluating i mu is that the domain mathscr d is generally not known explicitly in this paper we prove a theorem which allows us to restrict the calculation of the infimum to a nice subdomain we then apply this general result to diffusion processes with boundaries

a note on a minimax rule for portfolio selection and equilibrium price system this paper concerns a minimax model to investigate the optimal portfolio selection problem without riskless assets and with or without short sale restriction a numerical solution to the problem with short sale restriction is obtained by using the maximum entropy algorithm for the problem without short sale restriction we derive a analytical expression for the optimal solution a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system and an explicit formula for the price system furthermore a numerical example is given to show the validity of the method

dynamic portfolio optimization with risk control for absolute deviation model in this paper we present a new multiperiod portfolio selection with maximum absolute deviation model the investor is assumed to seek an investment strategy to maximize his her terminal wealth and minimize the risk one typical feature is that the absolute deviation is employed as risk measure instead of classical mean variance method furthermore risk control is considered in every period for the new model an analytical optimal strategy is obtained in a closed form via dynamic programming method algorithm with some examples is also presented to illustrate the application of this model

carne varopoulos bounds for centered random walks we extend the carne varopoulos upper bound on the probability transitions of a markov chain to a certain class of nonreversible processes by introducing the definition of a centering measure in the case of random walks on a group we study the connections between different notions of centering

brief paper parameter identification for nonlinear systems guaranteed confidence regions through lscr in this paper we consider the problem of constructing confidence regions for the parameters of nonlinear dynamical systems the proposed method uses higher order statistics and extends the lscr leave out sign dominant correlation regions algorithm for linear systems introduced in campi and weyer 2005 guaranteed non asymptotic confidence regions in system identification automatica 41 10 1751 1764 extended version available at the confidence regions contain the true parameter value with a guaranteed probability for any finite number of data points moreover the confidence regions shrink around the true parameter value as the number of data points increases the usefulness of the proposed approach is illustrated on some simple examples

doob s conditioned diffusions and their lifetimes on utilise les resultats de donsker et varadhan pour montrer que la queue de la distribution de la duree de vie decroit exponentiellement

condensation of non reversible zero range processes in this article we investigate the condensation phenomena for a class of non reversible zero range processes on a fixed finite set by establishing a novel inequality bounding the capacity between two sets and by developing a robust framework to perform quantitative analysis on the metastability of non reversible processes we prove that the condensed site of the corresponding zero range processes approximately behaves as a markov chain on the underlying graph whose jump rate is proportional to the capacity with respect to the underlying random walk the results presented in the current paper complete the generalization of the work of beltran and landim probab theory relat fields 152 781 807 2012 on reversible zero range processes and that of landim commun math phys 330 1 32 2014 on totally asymmetric zero range processes on a one dimensional discrete torus

on robust optimization of two stage systems robust optimization models belong to a special class of stochastic programs where the traditional expected cost minimization objective is replaced by one that explicitly addresses cost variability this paper explores robust optimization in the context of two stage planning systems we show that under arbitrary measures for variability the robust optimization approach might lead to suboptimal solutions to the second stage planning problem as a result the variability of the second stage costs may be underestimated thereby defeating the intended purpose of the model we propose sufficient conditions on the variability measure to remedy this problem under the proposed conditions a robust optimization model can be efficiently solved using a variant of the l shaped decomposition algorithm for traditional stochastic linear programs we apply the proposed framework to standard stochastic programming test problems and to an application that arises in auctioning excess electric power

assessing the quality of identified models through the asymptotic theory when is the result reliable in this paper the problem of estimating uncertainty regions for identified models is considered a typical approach in this context is to resort to the asymptotic theory of prediction error methods for system identification by means of which ellipsoidal uncertainty regions can be constructed for the uncertain parameters we show that the uncertainty regions worked out through the asymptotic theory can be unreliable in certain situations precisely characterized in the paper then we critically analyze the theoretical conditions for the validity of the asymptotic theory and prove that the asymptotic theory also applies under new assumptions which are less restrictive than the usually required ones thanks to this result we single out the classes of models among standard ones arx armax box jenkins etc where the asymptotic theory can be safely used in practical applications to assess the quality of the identified model these results are of interest in many applications including iterative controller design schemes

large scale mv efficient frontier computation via a procedure of parametric quadratic programming abstract despite the volume of research conducted on efficient frontiers in many cases it is still not the easiest thing to compute a mean variance mv efficient frontier even when all constraints are linear this is particularly true of large scale problems having dense covariance matrices and hence they are the focus in this paper because standard approaches for constructing an efficient frontier one point at a time tend to bog down on dense covariance matrix problems with many more than about 500 securities we propose as an alternative a procedure of parametric quadratic programming for more effective usage on large scale applications with the proposed procedure we demonstrate through computational results on problems in the 1000 3000 security range that the efficient frontiers of dense covariance matrix problems in this range are now not only solvable but can actually be computed in quite reasonable time

asymptotic properties of sps confidence regions abstract sign perturbed sums sps is a system identification method that constructs non asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions one of its main features is that for any finite number of data points and any user specified probability the constructed confidence region contains the true system parameter with exactly the user chosen probability in this paper we examine the size and the shape of the confidence regions and we show that the regions are strongly consistent i e they almost surely shrink around the true parameter as the number of data points increases furthermore the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory the results are also illustrated by a simulation example

an algebraic approach to integer portfolio problems abstract integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model we propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix to reach an optimal portfolio it is an essential ingredient the computation of different test sets via grobner basis of linear subproblems that are used in a dual search strategy

homogeneous nucleation for glauber and kawasaki dynamics in large volumes at low temperatures in this paper we study metastability in large volumes at low temperatures we consider both ising spins subject to glauber spin flip dynamics and lattice gas particles subject to kawasaki hopping dynamics let denote the inverse temperature and let c 2 be a square box with periodic boundary conditions such that lim we run the dynamics on starting from a random initial configuration where all of the droplets clusters of plus spins and clusters of particles respectively are small for large and for interaction parameters that correspond to the metastable regime we investigate how the transition from the metastable state with only small droplets to the stable state with one or more large droplets takes place under the dynamics this transition is triggered by the appearance of a single critical droplet somewhere in using potential theoretic methods we compute the average nucleation time the first time a critical droplet appears and starts growing up to a multiplicative factor that tends to 1 as it turns out that this time grows as ke for glauber dynamics and as k e for kawasaki dynamics where is the local canonical resp grand canonical energy to create a critical droplet and k is a constant reflecting the geometry of the critical droplet provided these times tend to infinity which puts a growth restriction on the fact that the average nucleation time is inversely proportional to is referred to as homogeneous nucleation because it says that the critical droplet for the transition appears essentially independently in small boxes that partition

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

perturbed datasets methods for hypothesis testing and structure of corresponding confidence sets hypothesis testing methods that do not rely on exact distribution assumptions have been emerging lately the method of sign perturbed sums sps is capable of characterizing confidence regions with exact confidence levels for linear regression and linear dynamical systems parameter estimation problems if the noise distribution is symmetric this paper describes a general family of hypothesis testing methods that have an exact user chosen confidence level based on finite sample count and without relying on an assumed noise distribution it is shown that the sps method belongs to this family and we provide another hypothesis test for the case where the symmetry assumption is replaced with exchangeability in the case of linear regression problems it is shown that the confidence regions are connected bounded and possibly non convex sets in both cases to highlight the importance of understanding the structure of confidence regions corresponding to such hypothesis tests it is shown that confidence sets for linear dynamical systems parameter estimates generated using the sps method can have non connected parts which have far reaching consequences

a dirichlet principle for non reversible markov chains and some recurrence theorems we extend the dirichlet principle to non reversible markov processes on countable state spaces we present two variational formulas for the solution of the poisson equation or equivalently for the capacity between two disjoint sets as an application we prove a some recurrence theorems in particular we show the recurrence of two dimensional cycle random walks under a second moment condition on the winding numbers

multi objective possibilistic model for portfolio selection with transaction cost in this paper we introduce the possibilistic mean value and variance of continuous distribution rather than probability distributions we propose a multi objective portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation for quantifying any potential return and risk portfolio liquidity is taken into account and a multi objective non linear programming model for portfolio rebalancing with transaction cost is proposed the models are illustrated with numerical examples

multidimensional random walks in random environments with subclassical limiting behavior in this paper we will describe and analyze a class of multidimensional random walks in random environments which contain the one dimensional nearest neighbor situation as a special case and have the pleasant feature that quite a lot can be said about them our results make rigorous a heuristic argument of marinari et al 1983 and show that in anyd we can have a xn is recurrent and b xn logn 2

genetic algorithms for portfolio selection problems with minimum transaction lots abstract conventionally portfolio selection problems are solved with quadratic or linear programming models however the solutions obtained by these methods are in real numbers and difficult to implement because each asset usually has its minimum transaction lot methods considering minimum transaction lots were developed based on some linear portfolio optimization models however no study has ever investigated the minimum transaction lot problem in portfolio optimization based on markowitz model which is probably the most well known and widely used based on markowitz model this study presents three possible models for portfolio selection problems with minimum transaction lots and devises corresponding genetic algorithms to obtain the solutions the results of the empirical study show that the portfolios obtained using the proposed algorithms are very close to the efficient frontier indicating that the proposed method can obtain near optimal and also practically feasible solutions to the portfolio selection problem in an acceptable short time one model that is based on a fuzzy multi objective decision making approach is highly recommended because of its adaptability and simplicity

metastability in a condensing zero range process in the thermodynamic limit zero range processes with decreasing jump rates are known to exhibit condensation where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value we study such a process on a one dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed super critical particle density we show that the process exhibits metastability with respect to the condensate location i e the suitably accelerated process of the rescaled location converges to a limiting markov process on the unit torus this process has stationary independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice our result extends previous work for fixed lattices and diverging density in beltran and landim probab theory relat fields 152 3 4 781 807 2012 and we follow the martingale approach developed there and in subsequent publications besides additional technical difficulties in estimating error bounds for transition rates the thermodynamic limit requires new estimates for equilibration towards a suitably defined distribution in metastable wells corresponding to a typical set of configurations with a particular condensate location the total exit rates from individual wells turn out to diverge in the limit which requires an intermediate regularization step using the symmetries of the process and the regularity of the limit generator another important novel contribution is a coupling construction to provide a uniform bound on the exit rates from metastable wells which is of a general nature and can be adapted to other models

crossing estimates and convergence of dirichlet functions along random walk and diffusion paths let x n be a transient reversible markov chain and let f be a function on the state space with finite dirichlet energy we prove crossing inequalities for the process f x n n geq 1 and show that it converges almost surely and in l 2 analogous results are also established for reversible diffusions on riemannian manifolds

nonlinear chance constrained problems with applications to hydro scheduling we present a branch and cut algorithm for a class of nonlinear chance constrained mathematical optimization problems with a finite number of scenarios unsatisfied scenarios can enter a recovery mode this class corresponds to problems that can be reformulated as deterministic convex mixed integer nonlinear programming problems with indicator variables and continuous scenario variables but the size of the reformulation is large and quickly becomes impractical as the number of scenarios grows the branch and cut algorithm is based on an implicit benders decomposition scheme where we generate cutting planes as outer approximation cuts from the projection of the feasible region on suitable subspaces the size of the master problem in our scheme is much smaller than the deterministic reformulation of the chance constrained problem we apply the branch and cut algorithm to the mid term hydro scheduling problem for which we propose a chance constrained formulation a computational study using data from ten hydroplants in greece shows that the proposed methodology solves instances faster than applying a general purpose solver for convex mixed integer nonlinear programming problems to the deterministic reformulation and scales much better with the number of scenarios

a minimax portfolio selection rule with linear programming solution a new principle for choosing portfolios based on historical returns data is introduced the optimal portfolio based on this principle is the solution to a simple linear programming problem this principle uses minimum return rather than variance as a measure of risk in particular the portfolio is chosen that minimizes the maximum loss over all past observation periods for a given level of return this objective function avoids the logical problems of a quadratic nonmonotone utility function implied by mean variance portfolio selection rules the resulting minimax portfolios are diversified for normal returns data the portfolios are nearly equivalent to those chosen by a mean variance rule framing the portfolio selection process as a linear optimization problem also makes it feasible to constrain certain decision variables to be integer or 0 1 valued this feature facilitates the use of more complex decision making models including models with fixed transaction charges and models with boolean type constraints on allocations

non asymptotic confidence sets for the parameters of linear transfer functions we consider the problem of constructing confidence sets for the parameters of input output transfer functions based on observed data the assumptions on the noise affecting the system are reduced to a minimum the noise can virtually be anything but in return the user must be able to select the input signal in this paper a procedure for solving this problem is developed in the general framework of leave out sign dominant confidence regions the procedure returns confidence regions that are guaranteed to contain the true transfer function with a user chosen probability for any finite data set

the rate function of hypoelliptic diffusions let be a hypoelliptic diffusion operator on a compact manifold m given an a priori smooth reference measure on m we can then rewrite l as the sum of a symmetric part l0 and a first order drift part y the paper investigates the effect of the drift y on the donsker varadhan rate function corresponding to the large deviations of the empirical measure of the diffusion when y is in the linear span of the first and second order lie brackets of the xi s we derive an affine bound relating the rate functions associated with l and l0 as soon as one point exists where y is not in the linear span of the first and second order lie brackets of the xi s we show that such an affine bound is impossible 1994 john wiley sons inc

metastability of reversible condensed zero range processes on a finite set let r s x s r be the jump rates of an irreducible random walk on a finite set s reversible with respect to some probability measure m for alpha 1 let g n r be given by g 0 0 g 1 1 g k k k 1 alpha k 2 consider a zero range process on s in which a particle jumps from a site x occupied by k particles to a site y at rate g k r x y let n stand for the total number of particles in the stationary state as n up arrow infinity all particles but a finite number accumulate on one single site we show in this article that in the time scale n1 alpha the site which concentrates almost all particles evolves as a random walk on s whose transition rates are proportional to the capacities of the underlying random walk

enhancing a branch and bound algorithm for two stage stochastic integer network design based models in this paper we present branch and bound b b strategies for two stage stochastic integer network design based models with integrality constraints in the first stage variables these strategies are used within l shaped decomposition based b b framework we propose a valid inequality in order to improve b b performance we use this inequality to implement a multirooted b b tree a selective use of optimality cuts is explored in the b b approach and we also propose a subgradient based technique for branching on 0 1 feasible solutions finally we present computational results for a fixed charge network design problem with random demands

metastability of nonreversible random walks in a potential field and the eyring kramers transition rate formula we consider nonreversible random walks in a bounded domain of d evolving on a potential field we describe the complete metastable behavior of the random walk among the landscape of valleys and we derive the eyring kramers formula for the mean transition time from a metastable set to a stable set 2017 wiley periodicals inc

guaranteed non asymptotic confidence regions in system identification in this paper we consider the problem of constructing confidence regions for the parameters of identified models of dynamical systems taking a major departure from the previous literature on the subject we introduce a new approach called leave out sign dominant correlation regions lscr which delivers confidence regions with guaranteed probability all results hold rigorously true for any finite number of data points and no asymptotic theory is involved moreover prior knowledge on the noise affecting the data is reduced to a minimum the approach is illustrated on several simulation examples showing that it delivers practically useful confidence sets with guaranteed probabilities

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

two pairs of families of polyhedral norms versus ell _p lp norms proximity and applications in optimization this paper studies four families of polyhedral norms parametrized by a single parameter the first two families consist of the cvar norm which is equivalent to the d norm or the largest k k norm and its dual norm while the second two families consist of the convex combination of the ell 1 l1 and ell infty l norms referred to as the deltoidal norm and its dual norm these families contain the ell 1 l1 and ell infty l norms as special limiting cases these norms can be represented using linear programming lp and the size of lp formulations is independent of the norm parameters the purpose of this paper is to establish a relation of the considered lp representable norms to the ell p lp norm and to demonstrate their potential in optimization on the basis of the ratio of the tight lower and upper bounds of the ratio of two norms we show that in each dual pair the primal and dual norms can equivalently well approximate the ell p lp and ell q lq norms respectively for p q in 1 infty p q 1 satisfying 1 p 1 q 1 1 p 1 q 1 in addition the deltoidal norm and its dual norm are shown to have better proximity to the ell p lp norm than the cvar norm and its dual numerical examples demonstrate that lp solutions with optimized parameters attain better approximation of the ell 2 l2 norm than the ell 1 l1 and ell infty l norms do

large scale portfolio optimization this paper describes a practical algorithm for large scale mean variance portfolio optimization the emphasis is on developing an efficient computational approach applicable to the broad range of portfolio models employed by the investment community what distinguishes these from the usual quadratic program is i the form of the covariance matrix arising from the use of factor and scenario models of return and ii the inclusion of transactions limits and costs a third aspect is the question of whether the problem should be solved parametrically in the risk reward trade off parameter or separately for several discrete values of we show how the parametric algorithm can be made extremely efficient by sparsifying the covariance matrix with the introduction of a few additional variables and constraints and by treating the transaction cost schedule as an essentially nonlinear nondifferentiable function then we show how these two seemingly unrelated approaches can be combined to yield good approximate solutions when minimum trading size restrictions buy or sell at least a certain amount or not at all are added in combination these approaches make possible the parametric solution of problems on a scale not heretofore possible on computers where cpu time and storage are the constraining factors

objective comparisons of the optimal portfolios corresponding to different utility functions abstract this paper considers the effects of some frequently used utility functions in portfolio selection by comparing the optimal investment outcomes corresponding to these utility functions assets are assumed to form a complete market of the black scholes type under consideration are four frequently used utility functions the power logarithm exponential and quadratic utility functions to make objective comparisons the optimal terminal wealths are derived by integration representation the optimal strategies which yield optimal values are obtained by the integration representation of a brownian martingale the explicit strategy for the quadratic utility function is new the strategies for other utility functions such as the power and the logarithm utility functions obtained this way coincide with known results obtained from merton s dynamic programming approach