riccati differential equation in optimal filtering of periodic non stabilizable systems this paper discusses the periodic solutions of the matrix riccati differential equation in the optimal filtering of periodic systems special emphasis is given to non stabilizable systems and the question addressed is the existence and uniqueness of a steady state periodic non negative definite solution of the periodic riccati differential equation which gives rise to an asymptotically stable steady state filter the results presented show that the stabilizability is not a necessary condition for the existence of such a periodic solution the convergence of the general solution of the periodic riccati differential equation to a periodic equilibrium solution is also investigated the results are extensions of existing time invariant systems results to the case of periodic systems

global attractivity for discrete models of nonautonomous logistic equations consider the following discrete model of a nonautonomous logistic equation n n 1 n n exp c n j 0mb j n n n j n 0 n 0 n 0 0andn j n j 0 1 j m where c n and b j n 0 j m n 0 are bounded and c n 0 b 0 n 0 b j n 0 1 j m n 0 in this paper using some kind of iterative method to the above equation we establish sufficient conditions that ensure the global attractivity for solutions the result is an extension of the former work k uesugi y muroya e ishiwata on the global attractivity for a logistic equation with piecewise constant arguments j math anal appl 294 2004 560 580 to the nonautonomous case

measures of risk the conditions under which the classical measures of risk like the mean the linear correlation coefficient and var can be used are discussed the definition of risk measure and the main recently proposed risk measures are presented the problems connected with co dependence are outlined

index tracking and enhanced indexing using mixed conditional value at risk abstract index tracking it and enhanced indexing ei are two forms of investment strategies which revolve around the movements of the benchmark index while it aims to match the performance of the benchmark index ei intents to outperform the same in this paper we seek to design portfolios for it and ei problems using mixed conditional value at risk mcvar we propose to use the two tail mcvar tmcvar measure to track the index optimizing tmcvar is a linear program which minimizes the upper deviation and the downside deviation from the benchmark index and hence meets the objective of it on the other hand we propose a two step procedure for ei problem in step one we design a discrete markov chain model to filter a few stocks on the basis of their high probability of gain over the benchmark index in step two we assign optimal weights to the filtered assets through maximizing any of the two variants of the starr ratio with mcvar or the starr ratio with deviation mcvar dmcvar maximizing the starr ratio either with mcvar or dmcvar is a linear program and hence tractable we analyze the empirical performance of the proposed models over 17 world wide indices using the rolling window approach we consider two it and four ei models from the literature for a comparative analysis it is exhibited that the proposed it model outperforms the other two it models over several performance measures including higher correlation value with the benchmark index and lower tracking error and the two proposed ei models outperform the other four ei models in achieving higher excess mean returns from the benchmark index

differential periodic riccati equations a note on the existence of an infinite number of periodic strong solutions abstract the differential matrix riccati equation with periodic coefficients is considered it is shown by means of a counter example that a sufficient condition for the existence of an infinite number of periodic non negative definite solutions given in a previous paper is not appropriately stated a suitable adjustment of the assumptions allows one to work out rigorous sufficient conditions thanks to these results a necessary and sufficient condition for the existence of the periodic strong solution which relied on the incorrect condition can be shown to be still valid

the persistence and global attractivity in general nonautonomous discrete single species kolmogorov model with delays in this paper general nonautonomous discrete time single species kolmogorov model with delays is studied some sufficient conditions on the boundedness persistence permanence and global attractivity of solutions are established as application the discrete time nonautonomous delayed allee effect model is discussed the sufficient conditions on the permanence and global attractivity are obtained

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

global asymptotic stability beyond 3 2 type stability for a logistic equation with piecewise constant arguments abstract in this paper a logistic equation with multiple piecewise constant arguments is investigated in detail we generalize the approach in two papers k uesugi y muroya e ishiwata on the global attractivity for a logistic equation with piecewise constant arguments j math anal appl 294 2 2004 560 580 and y muroya e ishiwata n guglielmi global stability for nonlinear difference equations with variable coefficients j math anal appl 334 1 2007 232 247 and establish a new condition for the global stability of the equation their results are given as one of the special cases moreover we improve the 3 2 type stability condition under several dominance assumptions on the coefficients of the equation some examples and numerical simulations are also presented all of these examples show that there are several conditions for the global stability of the equation depending on the coefficients on the delay terms of the equation beyond the 3 2 type stability condition

periodic strong solutions of periodically time varying matrix riccati equations abstract generalized conditions for the existence of periodic strong solutions in periodically time varying matrix riccati equations are derived first the precise structure of eigenvalues on the unit circle of the transition matrix associated with the hamil tonian matrix and that of the corresponding generalized eigenvectors are clarified in relation to the quasi detectability and quasi stabilizability of the system then such analysis is applied for deriving the conditions for the existence of a unique periodic real symmetric and non negative definite solution in the periodically time varying matrix riccati equation

a mixed integer linear programming formulation of the optimal mean value at risk portfolio problem abstract in this paper we consider an extension of the markovitz model in which the variance has been replaced with the value at risk so a new portfolio optimization problem is formulated we showed that the model leads to an np hard problem but if the number of past observation t or the number of assets k are low e g fixed to a constant polynomial time algorithms exist furthermore we showed that the problem can be formulated as an integer programming instance when k and t are large and var is small as common in financial practice the computational results show that the problem can be solved in a reasonable amount of time

robust portfolio selection problems in this paper we show how to formulate and solve robust portfolio selection problems the objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters we introduce uncertainty structures for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second order cone programs and therefore the computational effort required to solve them is comparable to that required for solving convex quadratic programs moreover we show that these uncertainty structures correspond to confidence regions associated with the statistical procedures employed to estimate the market parameters finally we demonstrate a simple recipe for efficiently computing robust portfolios given raw market data and a desired level of confidence

new contractivity condition in a population model with piecewise constant arguments abstract in this paper we improve contractivity conditions of solutions for the positive equilibrium n 1 a i 0 m b i of the following differential equation with piecewise constant arguments d n t d t n t r t 1 a n t i 0 m b i n n i n t n 1 n 0 1 2 n 0 n 0 0 and n j n j 0 j 1 2 m where r t is a nonnegative continuous function on 0 r t 0 i 0 m b i 0 b i 0 i 0 1 2 m and a b 0 i 1 m b i in particular for the case a 0 and m 1 we really improve the known three type conditions of the contractivity for solutions of this model see for example y muroya a sufficient condition on global stability in a logistic equation with piecewise constant arguments hokkaido math j 32 2003 75 83 for the other case a 0 and m 1 under the condition j 1 m b j 2 b 0 a j 1 m b j 1 b 0 j 0 m b j the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author y muroya persistence contractivity and global stability in logistic equations with piecewise constant delays j math anal appl 270 2002 602 635 and others

credit risk optimization with conditional value at risk criterion this paper examines a new approach for credit risk optimization the model is based on the conditional value at risk cvar risk measure the expected loss exceeding value at risk cvar is also known as mean excess mean shortfall or tail var this model can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize cvar subject to trading and return constraints the credit risk distribution is generated by monte carlo simulations and the optimization problem is solved effectively by linear programming the algorithm is very efficient it can handle hundreds of instruments and thousands of scenarios in reasonable computer time the approach is demonstrated with a portfolio of emerging market bonds

handling cvar objectives and constraints in two stage stochastic models abstract based on the polyhedral representation of kunzi bay and mayer kunzi bay a mayer j 2006 computational aspects of minimizing conditional value at risk computational management science 3 3 27 we propose decomposition frameworks for handling cvar objectives and constraints in two stage stochastic models for the solution of the decomposed problems we propose special level type methods

persistence contractivity and global stability in logistic equations with piecewise constant delays abstract we establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium n 1 a i 0 m b i of the following differential equation with piecewise constant arguments dn t dt n t r t 1 an t i 0 m b i n n i n t n 0 1 2 n 0 n 0 0 and n j n j 0 j 1 2 m where r t is a nonnegative continuous function on 0 r t 0 i 0mbi 0 bi 0 i 0 1 2 m and a i 0mbi 0 these new conditions depend on a b0 and i 1mbi and hence these are other type conditions than those given by so and yu hokkaido math j 24 1995 269 286 and others in particular in the case m 0 and r t r 0 we offer necessary and sufficient conditions for the persistence and contractivity of solutions we also investigate the following differential equation with nonlinear delay terms dx t dt x t r t 1 ax t g x t x t 1 x t m t 0 x k k 0 0 k m and 0 0 where r t is a nonnegative continuous function on 0 r t 0 1 ax g x x x 0 has a unique solution x 0 and g x0 x1 xm c1 0 0 0

persistence and global stability for discrete models of nonautonomous lotka volterra type abstract consider the following discrete models of nonautonomous lotka volterra type n i p 1 n i p exp c i p a i p n i p j 1 n l 0 m a ij l p n j p k l 1 i n p 0 1 2 n i p n ip 0 p 0 and n i0 0 1 i n where each c i p a i p and a ij l p are bounded for p 0 and inf p 0 a i p 0 a ii 0 p 0 1 i n a ij l p 0 1 i j n 0 l m k 0 0 integers k l 0 1 l m in this paper to the above discrete system we apply the techniques offered by ahmad and lazer nonlinear anal 40 2000 37 49 and establish similar conditions of the persistence and global asymptotic stability of the system

stabilizability and detectability of linear periodic systems abstract in this paper four characterizations of stabilizability and detectability of linear periodic systems are considered two of them look as natural extensions of the classical definitions given for time invariant systems the remaining two are modal characterizations which turn out to be useful in the analysis of the periodic lyapunov and riccati equations it is shown that all these notions of stabilizability and detectability are in fact equivalent to each other one of the various definitions calls for the existence of the kalman canonical decomposition of periodic systems this issue is addressed in the appendix

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

global stability of discrete population models with time delays and fluctuating environment the global stability of a discrete population model of volterra type is studied the model incorporates time delays and allows for a fluctuating environment by linearization of the model at positive solutions and construction of liapunov functionals sufficient conditions are obtained to ensure a positive solution of the model is stable and attracts all positive solutions

on the global attractivity for a logistic equation with piecewise constant arguments in this paper we consider the following logistic equation with piecewise constant arguments dn t dt rn t 1 j 0majn t j t 0 m 1 n 0 n0 0 n j n j 0 j 1 2 m where r 0 a0 a1 am 0 j 0maj 0 and x means the maximal integer not greater than x the sequence nn n 0 where nn n n n 0 1 2 satisfies the difference equation nn 1 nnexpr1 j 0majnn j n 0 1 2 under the condition that the first term a0 dominates the other m coefficients ai 1 i m we establish new sufficient conditions of the global asymptotic stability for the positive equilibrium n 1 j 0maj

measuring the coupled risks a copula based cvar model integrated risk management for financial institutions requires an approach for aggregating risk types such as market and credit whose distributional shapes vary considerably the financial institutions often ignore risks coupling influence so as to underestimate the financial risks we constructed a copula based conditional value at risk cvar model for market and credit risks this technique allows us to incorporate realistic marginal distributions that capture essential empirical features of these risks such as skewness and fat tails while allowing for a rich dependence structure finally the numerical simulation method is used to implement the model our results indicate that the coupled risks for the listed company s stock maybe are undervalued if credit risk is ignored especially for the listed company with bad credit quality