on weak solutions of forward backward sdes in this paper we continue exploring the notion of weak solution of forward backward stochastic differential equations fbsdes and associated forward backward martingale problems fbmps the main purpose of this work is to remove the constraints on the martingale integrands in the uniqueness proofs in our previous work ma et al in ann probab 36 6 2092 2125 2008 we consider a general class of non degenerate fbsdes in which all the coefficients are assumed to be essentially only bounded and uniformly continuous and the uniqueness is proved in the space of all the square integrable adapted solutions the standard solution space in the fbsde literature a new notion of semi strong solution is introduced to clarify the relations among different definitions of weak solution in the literature and it is in fact instrumental in our uniqueness proof as a by product we also establish some a priori estimates of the second derivatives of the solution to the decoupling quasilinear pde

entropy solutions to a strongly degenerate anisotropic convection diffusion equation with application to utility theory we study the deterministic counterpart of a backward forward stochastic differential utility which has recently been characterized as the solution to the cauchy problem related to a pde of degenerate parabolic type with a conservative first order term we first establish a local existence result for strong solutions and a continuation principle and we produce a counterexample showing that in general strong solutions fail to be globally smooth afterward we deal with discontinuous entropy solutions and obtain the global well posedness of the cauchy problem in this class eventually we select a sufficient condition of geometric type which guarantees the continuity of entropy solutions for special initial data as a byproduct we establish the existence of an utility process which is a solution to a backward forward stochastic differential equation for a given class of final utilities which is relevant for financial applications

linear quadratic partially observed forward backward stochastic differential games and its application in finance abstract this paper is concerned with a partially observed linear quadratic game problem driven by forward backward stochastic differential equations where the forward diffusion coefficients do not contain control variables and the control domains are not necessarily convex the drift term of the observation equation is linear with respect to the state and there is correlated noise between the state and the observation equation by virtue of the classical spike variational method and the backward separation technique we derive a necessary and a sufficient condition of the stochastic differential game problem then we obtain filtering equations and present a feedback representation form of the equilibrium point through riccati equations as a practical application we solve a partial information investment problem involving g expectation as a convex risk measurement and give the numerical simulation to show the explicit investment strategy and illustrate some reasonable phenomena influenced by common financial parameters

stochastic uncertain systems subject to relative entropy constraints induced norms and monotonicity properties of minimax games entropy and relative entropy are fundamental concepts on which information theory is founded on and in general telecommunication systems design on the other hand dissipation inequalities minimax strategies and induced norms are the basic concepts on which robustness of uncertain control and estimation of systems are founded on in this paper the precise relation between these notions is investigated in particular it will be shown that the higher the dissipation the higher the entropy of the system which has implications in computing the induced norm associated with robustness these connections are obtained by considering stochastic optimal uncertain control systems in which uncertainty is described by a relative entropy constraint between the nominal and uncertain measures while the pay off is a linear functional of the uncertain measure this is a minimax game in which the controller measure seeks to minimize the pay off while the disturbance measure aims at maximizing the pay off salient properties of the minimax solution are derived including a characterization of the optimal sensitivity reduction computation of the induced norm monotonicity properties of minimax solution and relations between dissipation and relative entropy of the system the theory is developed in an abstract setting and then applied to nonlinear partially observable continuous time uncertain controlled systems in which the nominal and uncertain systems are described by conditional distributions in addition existence of the optimal control policy among the class of policies known as wide sense control laws is shown and an explicit formulae for the worst case conditional measure is derived the results are applied to linear quadratic gaussian problems

partial information state based optimization of partially observable markov decision processes and the separation principle we propose a partial information state based approach to the optimization of the long run average performance in a partially observable markov decision process pomdp in this approach the information history is summarized at least partially by a or a few statistic s not necessary sufficient called a partial information state and actions depend on the partial information state rather than system states we first propose the single policy based comparison principle under which we derive an hjb type of optimality equation and policy iteration for the optimal policy in the partial information state based policy space we then introduce the q sufficient statistics and show that if the partial information state is q sufficient then the optimal policy in the partial information state based policy space is optimal in the space of all feasible information state based policies we show that with some further conditions the well known separation principle holds the results are obtained by applying the direct comparison based approach initially developed for discrete event dynamic systems

variational processes from the weak forward equation in this paper the author constructs markov diffusion processes from a given system of borel probability measures on ad dimensional euclidean space he constructs a so called variational process which does not always coincide with a nelson process he also discusses schrodinger s problem in quantum mechanics

kalman bucy filtering equations of forward and backward stochastic systems and applications to recursive optimal control problems abstract this paper is concerned with kalman bucy filtering problems of a forward and backward stochastic system which is a hamiltonian system arising from a stochastic optimal control problem there are two main contributions worthy pointing out one is that we obtain the kalman bucy filtering equation of a forward and backward stochastic system and study a kind of stability of the aforementioned filtering equation the other is that we develop a backward separation technique which is different to wonham s separation theorem to study a partially observed recursive optimal control problem this new technique can also cover some more general situation such as a partially observed linear quadratic non zero sum differential game problem is solved by it we also give a simple formula to estimate the information value which is the difference of the optimal cost functionals between the partial and the full observable information cases

a filtering problem with uncertainty in observation abstract this paper is concerned with a generalized kalman bucy filtering model and corresponding robust problem under model uncertainty we find that this robust problem is equivalent to considering an estimate problem under some sublinear operator therefore we turn to obtaining the minimum mean square estimator under a sublinear operator by girsanov theorem and minimax theorem we obtain the optimal estimator x t of the signal process x t for given time t 0 t

the robust h sub 2 control problem a worst case design the worst case effect of a disturbance system on the h sub 2 norm of the system is analyzed an explicit expression is given for the worst case h sub 2 norm when the disturbance system is allowed to vary over all nonlinear time varying and possibly noncausal systems with bounded l sub 2 induced operator norm an upper bound for this measure which is equal to the worst case h sub 2 norm if the exogeneous input is scalar is defined some further analysis of this upper bound is done and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given the latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature

a partial information non zero sum differential game of backward stochastic differential equations with applications this paper is concerned with a new kind of non zero sum differential game of backward stochastic differential equations bsdes it is required that the control is adapted to a sub filtration of the filtration generated by the underlying brownian motion we establish a necessary condition in the form of maximum principle with pontryagin s type for open loop nash equilibrium point of this type of partial information game and then give a verification theorem which is a sufficient condition for nash equilibrium point the theoretical results are applied to study a partial information linear quadratic lq game and a partial information financial problem

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

semimartingale integral representation we provide an integral representation for smooth functionals of continuous semimartingales the representation is related to an infinite dimensional nonautonomous parabolic equation semimartingale integral representations including a martingale representation are given in terms of a solution to this equation

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

forward backward stochastic differential equations on infinite horizon and quasilinear elliptic pdes 2019 elsevier inc a class of infinite horizon forward backward stochastic differential equations fbsdes is investigated under some monotonicity conditions the existence and uniqueness of solutions in an arbitrarily large space for fbsdes on infinite horizon is obtained the probabilistic interpretations for a large class of quasilinear elliptic partial differential equations pdes in a global space is then given by virtue of the solutions of fbsdes on infinite horizon

state distributions and minimum relative entropy noise sequences in uncertain stochastic systems the discrete time case this paper is concerned with dissipativity theory and robust performance analysis and design of discrete time stochastic systems driven by statistically uncertain random noise the uncertainty is quantified by the conditional relative entropy of the actual probability law of the noise with respect to a nominal product measure corresponding to a white noise sequence we discuss a balance equation dissipation inequality and superadditivity property for the corresponding conditional relative entropy supply as a function of time the problem of minimizing the supply required to drive the system between given state distributions over a specified time horizon is considered such variational problems involving entropy and probabilistic boundary conditions are known in the literature as schrodinger bridge problems in application to control systems the minimum required conditional relative entropy supply characterizes the robustness of the system with respect to a statistically uncertain random noise we o

a robust kalman bucy filtering problem abstract a generalized kalman bucy model under model uncertainty and a corresponding robust problem are studied in this paper we find that this robust problem is equivalent to an estimated problem under a sublinear operator by girsanov transformation and the minimax theorem we prove that this problem can be reformulated as a classical kalman bucy filtering problem under a new probability measure the equation which governs the optimal estimator is obtained moreover the optimal estimator can be decomposed into the classical optimal estimator and a term related to the model uncertainty parameter under some condition

singular stochastic control and optimal stopping with partial information of ito levy processes we study partial information possibly non markovian singular stochastic control of ito levy processes and obtain general maximum principles the results are used to find connections between singular stochastic control reflected backward stochastic differential equations and optimal stopping in the partial information case as an application we give an explicit solution to a class of optimal stopping problems with finite horizon and partial information

robust image corner detection through curvature scale space this paper describes a novel method for image corner detection based on the curvature scale space css representation the first step is to extract edges from the original image using a canny detector 1986 the corner points of an image are defined as points where image edges have their maxima of absolute curvature the corner points are detected at a high scale of the css and tracked through multiple lower scales to improve localization this method is very robust to noise and we believe that it performs better than the existing corner detectors an improvement to canny edge detector s response to 45 spl deg and 135 spl deg edges is also proposed furthermore the css detector can provide additional point features curvature zero crossings of image edge contours in addition to the traditional corners

state space approach to discrete time h control abstract state space solutions to a discrete time problem are given for a given number 0we give a characterization of all controllers such that the norm of the closed loop transfer function is less than the approach taken is based on the solution of two riccati equations using the stable deflating subspace of a symplectic pencil this ensures that no unnecessary assumptions on the a matrix on the realization of the transfer function are needed while the results are the direct analogues of those in the continuous time the state space derivation is considerably more difficult

backward doubly stochastic differential equations with weak assumptions on the coefficients in this paper we deal with one dimensional backward doubly stochastic differential equations bdsdes we obtain existence theorems and comparison theorems for solutions of bdsdes with weak assumptions on the coefficients

a stable multistep scheme for solving backward stochastic differential equations in this paper we propose a stable multistep scheme on time space grids for solving backward stochastic differential equations in our scheme the integrands which are conditional mathematical expectations derived from the original equations are approximated by using lagrange interpolating polynomials with values of the integrands at multiple time levels they are then numerically evaluated using the gauss hermite quadrature rules and polynomial interpolations on the spatial grids error estimates are rigorously proved for the semidiscrete version of the proposed scheme for backward stochastic differential equations with certain types of simplified generator functions finally various numerical examples and comparisons with some other methods are presented to demonstrate high accuracy of the proposed multistep scheme

on semi linear degenerate backward stochastic partial differential equations in this paper we study a class of one dimensional degenerate semilinear backward stochastic partial differential equations bspdes for short of parabolic type by establishing some new a priori estimates for both linear and semilinear bspdes we show that the regularity and uniform boundedness of the adapted solution to the semilinear bspde can be determined by those of the coefficients a special feature that one usually does not expect from a stochastic differential equation the proof follows the idea of the so called bootstrap method which enables us to analyze each of the derivatives of the solution under consideration some related results including some comparison theorems of the adapted solutions for semilinear bspdes as well as a nonlinear stochastic feynman kac formula are also given

acord an adaptive corner detector for planar curves abstract in contrast to the conventional method of smoothing a curve at multiple scales and integrating the information at various scales a technique for smoothing a curve adaptively based on the roughness present in the curve is suggested the procedure does not require smoothing at all levels of detail and it does not require construction of complete scale space map and representation of the map by tree the procedure has been applied on a number of digital curves and the results have been compared with those of the recent work

solving bsde with adaptive control variate we present and analyze an algorithm to solve numerically bsdes based on picard s iterations and on a sequential control variate technique its convergence is geometric moreover the solution provided by our algorithm is regular both w r t time and space

on the relative entropy of discrete time markov processes with given end point densities given a markov process x k defined over a finite interval i 0 n i spl sub z we construct a process x k with the same initial density as x but a different end point density which minimizes the relative entropy of x and x it is shown that x is a markov process in the same reciprocal class as x in the gaussian case the minimum relative entropy problem is related to a minimum energy lqg optimal control problem

analysis of robust h 2 performance using multiplier theory in this paper the problem of determining the worst case h2 performance of a control system subject to linear time invariant uncertainties is considered a set of upper bounds on the performance is derived based on the theory of stability multipliers and the solution of an original optimal control problem the numerical issues raised by the resulting computational problems are discussed in particular newly developed interior point convex optimization methods combined with linear matrix inequalities apply very well to the fast and accurate solution of these problems the new results compare favorably with prior ones the method can be extended to other types of perturbations

new method to find corner and tangent vertices in sketches using parametric cubic curves approximation some recent approaches have been presented as simple and highly accurate corner finders in the sketches including curves which is useful to support natural human computer interaction but these in most cases do not consider tangent vertices smooth points between two geometric entities present in engineering models what implies an important drawback in the field of design in this article we present a robust approach based on the approximation to parametric cubic curves of the stroke for further radius function calculation in order to detect corner and tangent vertices we have called our approach tangent and corner vertices detection tcvd and it works in the following way first corner vertices are obtained as minimum radius peaks in the discrete radius function where radius is obtained from differences second approximated piecewise parametric curves on the stroke are obtained and the analytic radius function is calculated then curves are obtained from stretches of the stroke that have a small radius finally the tangent vertices are found between straight lines and curves or between curves where no corner vertices are previously located the radius function to obtain curves is calculated from approximated piecewise curves which is much more noise free than discrete radius calculation several tests have been carried out to compare our approach to that of the current best benchmarked and the obtained results show that our approach achieves a significant accuracy even better finding corner vertices and moreover tangent vertices are detected with an accuracy near to 92 and a false positive rate near to 2

on the geometry of maximum entropy problems we show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite dimensional maximum entropy problems concerning probability distributions spectral densities and covariance matrices these include burg s spectral estimation method and dempster s covariance completion as well as various recent generalizations of the above we then apply this orthogonality principle to the new problem of completing a block circulant covariance matrix when an a priori estimate is available

numerical algorithms for forward backward stochastic differential equations efficient numerical algorithms are proposed for a class of forward backward stochastic differential equations fbsdes connected with semilinear parabolic partial differential equations as in j douglas jr j ma and p protter ann appl probab 6 1996 pp 940 968 the algorithms are based on the known four step scheme for solving fbsdes the corresponding semilinear parabolic equation is solved by layer methods which are constructed by means of a probabilistic approach the derivatives of the solution u of the semilinear equation are found by finite differences the forward equation is simulated by mean square methods of order 1 2 and 1 corresponding convergence theorems are proved along with the algorithms for fbsdes on a fixed finite time interval we also construct algorithms for fbsdes with random terminal time the results obtained are supported by numerical experiments

dual method for continuous time markowitz s problems with nonlinear wealth equations continuous time mean variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method a necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique it is also shown that the optimal wealth and portfolio is the solution of a forward backward stochastic differential equation with constraints

on the existence of optimal controls for spdes with boundary noise and boundary control we consider a stochastic optimal control problem for a heat equation with boundary noise and boundary control under suitable assumptions on the coefficients we prove existence of optimal controls in a strong sense by solving the related stochastic hamiltonian system

performance comparisons of contour based corner detectors corner detectors have many applications in computer vision and image identification and retrieval contour based corner detectors directly or indirectly estimate a significance measure e g curvature on the points of a planar curve and select the curvature extrema points as corners while an extensive number of contour based corner detectors have been proposed over the last four decades there is no comparative study of recently proposed detectors this paper is an attempt to fill this gap the general framework of contour based corner detection is presented and two major issues curve smoothing and curvature estimation which have major impacts on the corner detection performance are discussed a number of promising detectors are compared using both automatic and manual evaluation systems on two large datasets it is observed that while the detectors using indirect curvature estimation techniques are more robust the detectors using direct curvature estimation techniques are faster

quasi linear pdes and forward backward stochastic differential equations weak solutions abstract in this paper we study the existence uniqueness and the probabilistic representation of the weak solutions of quasi linear parabolic and elliptic partial differential equations pdes in the sobolev space h 1 r d for this we study first the solutions of forward backward stochastic differential equations fbsdes with smooth coefficients regularity of solutions and their connection with classical solutions of quasi linear parabolic pdes then using the approximation procedure we establish their convergence in the sobolev space to the solutions of the fbsdes in the space l 2 r d r d l 2 r d r k l 2 r d r k d this gives a connection with the weak solutions of quasi linear parabolic pdes finally we study the unique weak solutions of quasi linear elliptic pdes using the solutions of the fbsdes on infinite horizon

anisotropy based performance analysis of linear discrete time invariant control systems the anisotropic norm of a linear discrete time invariant system measures system output sensitivity to stationary gaussian input disturbances of bounded mean anisotropy mean anisotropy characterizes the degree of predictability or colouredness and spatial non roundness of the noise the anisotropic norm falls between the h 2 and h infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known this paper develops a method for numerical computation of the anisotropic norm which involves linked riccati and lyapunov equations and an associated special type equation

on numerical approximations of forward backward stochastic differential equations a numerical method for a class of forward backward stochastic differential equations fbsdes is proposed and analyzed the method is designed around the four step scheme j douglas jr j ma and p protter ann appl probab 6 1996 pp 940 968 but with a hermite spectral method to approximate the solution to the decoupling quasi linear pde on the whole space a rigorous synthetic error analysis is carried out for a fully discretized scheme namely a first order scheme in time and a hermite spectral scheme in space of the fbsdes equally important a systematical numerical comparison is made between several schemes for the resulting decoupled forward sde including a stochastic version of the adams bashforth scheme it is shown that the stochastic version of the adams bashforth scheme coupled with the hermite spectral method leads to a convergence rate of frac 32 in time which is better than those in previously published work for the fbsdes

minimax lqg control of stochastic partially observed uncertain systems we consider an infinite horizon linear quadratic minimax optimal control problem for stochastic uncertain systems with output measurement a new description of stochastic uncertainty is introduced using a relative entropy constraint for the stochastic uncertain system under consideration a connection between the worst case control design problem and a specially parametrized risk sensitive stochastic control problem is established using this connection a minimax optimal lqg controller is constructed which is based on a pair of algebraic matrix riccati equations arising in risk sensitive control it is shown that this minimax optimal controller absolutely stabilizes the stochastic uncertain system

bid price controls for network revenue management martingale characterization of optimal bid prices we consider a continuous time rate based model of network revenue management under mild assumptions we construct a simple e optimal bid price control which can be viewed as a perturbation of a bid price control in the classical sense williamson e l 1992 airline network seat control ph d thesis mit cambridge ma we show that the associated bid price process forms a martingale and the corresponding booking controls converge in an appropriate sense to an optimal control as e tends to 0 moreover we show that there exists an optimal generalized bid price control where the bid price process forms a martingale and is used in conjunction with a capacity usage limit process we also discuss its connection to the bid price controls in the classical sense and sufficient conditions for the near optimality of the latter

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

polygonal approximation of digital planar curves through break point suppression this paper presents a new algorithm that detects a set of dominant points on the boundary of an eight connected shape to obtain a polygonal approximation of the shape itself the set of dominant points is obtained from the original break points of the initial boundary where the integral square is zero for this goal most of the original break points are deleted by suppressing those whose perpendicular distance to an approximating straight line is lower than a variable threshold value the proposed algorithm iteratively deletes redundant break points until the required approximation which relies on a decrease in the length of the contour and the highest error is achieved a comparative experiment with another commonly used algorithm showed that the proposed method produced efficient and effective polygonal approximations for digital planar curves with features of several sizes

an adaptive method for detecting dominant points abstract in this paper we propose an adaptive method for the polygonal approximation of a digitized curve instead of setting a fixed length of support region in advance the new method will compute the suitable length of support region for each point to find the best approximated curvature the dominant points are identified as the points with local maximum curvatures in addition the break point detection is conducted to reduce the computations the experimental results show that the proposed method can approximate the curves effectively

dynamic output feedback control of the liouville equation for discrete time siso linear systems in this paper we address the so called liouville control problem for discrete time siso linear systems in the class of gaussian distributions in particular we propose a systematic procedure for the characterization of a dynamic output feedback policy that will transfer the output of the system which is a known gaussian random variable to a goal gaussian distribution after a finite number of stages in the proposed approach the liouville control problem is reduced to two decoupled finite dimensional quadratic programs one of which is subject to a single affine constraint which is a convex program whereas the other one is subject to a single quadratic equality constraint despite the fact that the second optimization problem is not convex one can characterize its exact solution via a systematic procedure without resorting to convex relaxation techniques which may yield suboptimal or even infeasible solutions to the original nonconvex optimization problem finally we present numerical simulations that illustrate the key ideas of this paper

a mean variance optimization problem for discounted markov decision processes in this paper we consider a mean variance optimization problem for markov decision processes mdps over the set of deterministic stationary policies different from the usual formulation in mdps we aim to obtain the mean variance optimal policy that minimizes the variance over a set of all policies with a given expected reward for continuous time mdps with the discounted criterion and finite state and action spaces we prove that the mean variance optimization problem can be transformed to an equivalent discounted optimization problem using the conditional expectation and markov properties then we show that a mean variance optimal policy and the efficient frontier can be obtained by policy iteration methods with a finite number of iterations we also address related issues such as a mutual fund theorem and illustrate our results with an example

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

solving forward backward stochastic differential equations explicitly a four step scheme in this paper we investigate the nature of the adapted solutions to a class of forward backward stochastic differential equations sdes for short in which the forward equation is non degenerate we prove that in this case the adapted solution can always be sought in an ordinary sense over an arbitrarily prescribed time duration via a direct four step scheme using this scheme we further prove that the backward components of the adapted solution are determined explicitly by the forward components via the solution of a certain quasilinear parabolic pde system moreover the uniqueness of the adapted solutions over an arbitrary time duration as well as the continuous dependence of the solutions on the parameters can all be proved within this unified framework some special cases are studied separately in particular we derive a new form of the integral representation of the clark haussmann ocone type for functionals or functions of diffusions in which the conditional expectation is no longer needed

mean variance portfolio selection under partial information this paper is concerned with a continuous time mean variance portfolio selection problem in a possibly incomplete market with multiple stocks and a bond only the past price movements of the stocks and the bond are the information available to the investors a separation principle is shown to hold in this setting efficient strategies based on the aforementioned partial information are derived which involve the optimal filter of the stock appreciation rate processes the main methodological contribution of the paper is to employ the particle system representation to develop analytical and numerical approaches in obtaining the filter as well as solving the related backward stochastic differential equation

maximum principles for a class of partial information risk sensitive optimal controls in this technical note we study a class of partial information risk sensitive optimal controls the main results are some necessary and sufficient conditions for these partial information control problems for illustration one example is proposed and then solved using our results

finite horizon robust state estimation for uncertain finite alphabet hidden markov models with conditional relative entropy constraints we consider a robust state estimation problem for time varying uncertain discrete time homogeneous first order finite state finite alphabet hidden markov models hmms a class of time varying uncertain hmms is considered in which the uncertainty is sequentially described by a conditional relative entropy constraint on perturbed conditional probability measures given a realized observation sequence for this class of uncertain hmms the robust state estimation problem is formulated as a constrained optimization problem using a lagrange multiplier technique and a variational formula for conditional relative entropy the above problem is converted into an unconstrained optimization problem and a problem related to partial information risk sensitive filtering a measure transformation technique and an information state method are employed to solve this equivalent problem related to risk sensitive filtering a characterization of the solution to the robust state estimation problem is also presented

forward backward stochastic differential equations with mixed initial terminal conditions well posedness of forward backward stochastic differential equations fbsdes for short in l p spaces with mixed initial terminal conditions is studied a notion of lyapunov operator is introduced whose existence leads to a priori estimates of the adapted solutions sufficient for the well posedness of the corresponding fbsdes via the method of continuation various situations are discussed under which lyapunov operators do exist

optimal control problem of backward stochastic differential delay equation under partial information abstract in this paper we study the optimal control problem of backward stochastic differential delay equation under partial information a class of time advanced stochastic differential equations asdes is introduced as the adjoint process via duality relation by means of asdes we suggest a maximum principle of this problem and obtain necessary and sufficient conditions of optimality we apply the theoretical results to study linear quadratic optimal control problem and obtain a forward backward stochastic differential filtering equation fbsdfe with time advanced forward equation that leads to optimal control at the same time some auxiliary filtering results and properties about time advanced sdes are also presented

linear quadratic stochastic differential games open loop and closed loop saddle points in this paper we consider a linear quadratic stochastic two person zero sum differential game the controls for both players are allowed to appear in both drift and diffusion of the state equation the weighting matrices in the performance functional are not assumed to be definite non singular the existence of an open loop saddle point is characterized by the existence of an adapted solution to a linear forward backward stochastic differential equation with constraints together with a convexity concavity condition and the existence of a closed loop saddle point is characterized by the existence of a regular solution to a riccati differential equation it turns out that there is a significant difference between open loop and closed loop saddle points also it is found that there is an essential feature that prevents a linear quadratic optimal control problem from being a special case of linear quadratic two person zero sum differential games

solution to discrete time linear fbsdes with application to stochastic control problem in this paper we consider a class of infinite horizon forward and backward stochastic difference equations fbsdes that are fully coupled the adapted solution is given by establishing an explicit relation between the forward and backward components in terms of a generalized algebraic riccati equation the equivalence between the exponential stabilizability of the stochastic control system and the infinite horizon fbsdes is derived as an application the fbsdes are used to characterize the maximum principle of the infinite horizon stochastic optimal control problem

on upper estimate of anisotropic norm of uncertain system with application to stochastic robust control abstractthis paper considers a stable linear discrete time invariant system with linear fractional norm bounded uncertainty an estimate of the anisotropic norm of this system is derived it is shown that the anisotropic norm is bounded above if a system of inequalities of certain kind is solvable this system consists of two linear matrix inequalities and inequality with respect to the determinant of a positive definite matrix by minimising the squared threshold value under constraints in form of the system of matrix inequalities one can obtain the upper estimate of the anisotropic norm of the considered system the introduced analysis result is directly applied to solve the problem of synthesis of state feedback robust anisotropic controller

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

polygonal representation of digital planar curves through dominant point detection a nonparametric algorithm we describe a new algorithm that detects a set of feature points on the boundary of an 8 connected shape that constitute the vertices of a polygonal approximation of the shape itself the set of feature points nodes is a ranked subset of the original shape points whose connected left and right arm extents cover the entire shape nodes are ranked based on their strength in terms of their importance to other boundary points length of support region and distance from the centroid the polygon obtained by linking the detected nodes approximates the contour in an intuitive way the proposed algorithm does not require an input parameter and works well for shapes with features of multiple sizes

comparison and improvement of tangent estimators on digital curves many contour based applications rely on the estimation of the geometry of the shape such as pattern recognition or classification methods this paper proposes a comprehensive evaluation on the problem of tangent estimators on digital curves the methods taken into account use different paradigms approximation and digital geometry in the former paradigm methods based on polynomial fitting smoothing and filtering are reviewed in the latter case of digital geometry we consider two methods that mainly rely on digital straight line recognition j o lachaud a vialard f de vieilleville fast accurate and convergent tangent estimation on digital contours image and vision computing 25 10 2007 1572 1587 and optimization b kerautret j o lachaud robust estimation of curvature along digital contours with global optimization in proceedings of discrete geometry for computer imagery lyon france lecture notes in computer science vol 4992 springer berlin 2008 the comparison takes into account objective criteria such as multi grid convergence average error maximum error isotropy and length estimation experiments underline that adaptive methods based on digital straight line recognition often propose a good trade off between time and precision and that if precision is to be sought non adaptive methods can be easily transformed into adaptive methods to get more accurate estimations

extraction of trend lines and extrema from multiscale curves abstract multiscale planar curves are curves conveying information at several levels of detail to extract polygonal approximations of such curves at different resolutions we propose a parallel method based on connecting locally computed centroids the implementation makes use of a new pyramidal data structure the chain pyramid coarser and coarser approximations are obtained through a hierarchy of increasingly coarse tessellations significant extrema of the curves are localized at the highest resolution by segmenting at a natural scale and employing the structure of the chain pyramid for down projection

stochastic target problems dynamic programming and viscosity solutions in this paper we define and study a new class of optimal stochastic control problems which is closely related to the theory of backward sdes and forward backward sdes the controlled process x nu y nu takes values in mathbb r d times mathbb r and a given initial data for x nu 0 then the control problem is to find the minimal initial data for y nu so that it reaches a stochastic target at a specified terminal time t the main application is from financial mathematics in which the process x nu is related to stock price y nu is the wealth process and nu is the portfolio we introduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation the boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense this provides a unique characterization of the value function which is the minimal initial data for y nu

minimax optimal control of stochastic uncertain systems with relative entropy constraints this paper considers a new class of discrete time stochastic uncertain systems in which the uncertainty is described by a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution this uncertainty description is a natural extension to the case of stochastic uncertain systems of the sum quadratic constraint uncertainty description this paper solves problems of worst case robust performance analysis and output feedback minimax optimal controller synthesis in a general nonlinear setting specializing these results to the linear case leads to a minimax linear quadratic gaussian lqg optimal controller this controller is defined by riccati difference equations and a kalman filter like state equation the paper also shows that the minimax lqg problem will have a solution if and only if a corresponding h sup spl infin control problem has a solution a linear example is presented to illustrate the minimax lqg methodology

quadratic hedging and mean variance portfolio selection with random parameters in an incomplete market this paper concerns the problems ofquadratic hedging andpricing andmean variance portfolio selection in anincomplete market setting with continuous trading multiple assets and brownian information in particular we assume throughout that the parameters describing the market model may be random processes we approach these problems from the perspective oflinear quadratic lq optimal control and backward stochastic differential equations bsdes that is we focus on the so calledstochastic riccati equation sre associated with the problem excepting certain special cases solvability of the sre remains an open question our primary theoretical contribution is a proof of existence and uniqueness of solutions of the sre associated with the quadratic hedging and mean variance problems in addition we derive closed form expressions for the optimal portfolios and efficient frontier in terms of the solution of the sre a generalization of themutual fund theorem is also obtained

finite horizon covariance control for discrete time stochastic linear systems subject to input constraints abstract this work deals with a finite horizon covariance control problem for discrete time stochastic linear systems with complete state information subject to input constraints first we present the main steps for the transcription of the covariance control problem which is originally formulated as a stochastic optimal control problem into a deterministic nonlinear program nlp with a convex performance index and with both convex and non convex constraints in particular the convex constraints in this nonlinear program are induced by the input constraints of the stochastic optimal control problem whereas the non convex constraints are induced by the requirement that the terminal state covariance be equal to a prescribed positive definite matrix subsequently we associate this nonlinear program via a simple convex relaxation technique with a convex semi definite program which can be solved numerically by means of modern computational tools of convex optimization although in general the endpoints of a representative sample of closed loop trajectories generated by the control policy that corresponds to the solution of the relaxed convex program are not expected to follow exactly the goal terminal gaussian distribution they are more likely to be concentrated near the mean of this distribution than if they were drawn from the latter which is a desirable feature in practice numerical simulations that illustrate the key ideas of this work are also presented

an interpolated stochastic algorithm for quasi linear pdes in this paper we improve the forward backward algorithm for quasi linear pdes introduced in a previous work the new discretization scheme takes advantage of the standing regularity properties of the true solution through an interpolation procedure for the convergence analysis we also exploit the optimality of the square gaussian quantization used to approximate the conditional expectations involved the resulting bound for the error is closely related to the holder exponent of the second order spatial derivatives of the true solution and turns out to be more satisfactory than the one previously established

mean variance criteria for finite continuous time markov decision processes this technical note deals with the mean variance problem known as the average variance av minimization problem for finite continuous time markov decision processes we first introduce a so called g condition which is weaker than the well known ergodicity and unichain conditions and sufficient for the finiteness of the av of a policy also we present an example of a policy having infinite av when the g condition is not satisfied under the g condition we prove that the av criterion can be transformed into an equivalent mean or expected average criterion by using a martingale technique and an observation from the canonical form of a transition rate matrix and thus the existence and calculation of an av minimal policy over a class of mean optimal policies are obtained by a policy iteration algorithm in an finite number of iterations as byproduct we obtain some interesting new results about the mean average optimality

on the viscosity solutions of a stochastic differential utility problem we prove existence uniqueness and gradient estimates of stochastic differential utility as a solution of the cauchy problem for the following equation in r 3 xxu u yu tu f u where f is lipschitz continuous we also characterize the solution in the vanishing viscosity sense r 2002 elsevier science usa all rights reserved

one order numerical scheme for forward backward stochastic differential equations a one order numerical scheme based on the four step scheme developed by ma et al for the adapted solutions to a class of forward backward stochastic differential equations is proposed and analyzed for the decoupling quasilinear parabolic equations a new kind of characteristics and finite difference method is used while for the decoupled forward sde we use the milstein scheme

state space formulae for discrete time h optimization abstract state space formulae and proofs are given for ail the important steps in discrete time h 8 optimization the steps closely follow the algorithms for continuous time systems but there are some technically involved differences in the detail that make their derivation non trivial

corner detection and curve segmentation by multiresolution chain code linking in this paper we propose a new method to characterise a curve by means of the hierarchical computation of a multiresolution structure this structure consisting of successive lower resolution versions of the same object is processed using the linked pyramid approach we adapt the multiresolution pixel linking algorithm to the processing of curve contours which are described by their chain code we also introduce a selective class selection process which allows application of the algorithm to segmentation and detection of contour features the resulting framework presents good performance for a wide range of object sizes without the need of any parameter tweaking and allows detection of shape detail at different scales

the maximum principle for global solutions of stochastic stackelberg differential games national science foundation dms 1303775 research grant council of the hksar cityu 500113

second order backward stochastic differential equations and fully nonlinear parabolic pdes for a d dimensional diffusion of the form dxt xt dt xt dwt and continuous functions f and g we study the existence and uniqueness of adapted processes y z and a solving the second order backward stochastic differential equation 2bsde dyt f t xt yt zt t dt z dxt t 0 t dzt at dt t dxt

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area