european option pricing with transaction costs the authors consider the problem of pricing european options in a market model similar to the black scholes one except that proportional transaction charges are levied on all sales and purchases o

spectral tests for observability and detectability of periodic markov jump systems with nonhomogeneous markov chain this paper addresses observability and detectability of discrete time periodic systems with nonhomogeneous markov jump parameter popov belevitch hautus pbh type criteria are proposed for the concerned structural properties it is shown that different from stochastic systems with constant coefficients or homogeneous markov chain the spectral criteria of considered plants do not rely on a single operator but on a finite sequence of linear evolution operators by use of the obtained detectability criterion an extended lyapunov theorem is established which relates asymptotic mean square stability to a periodic lyapunov equation further a difference riccati equation with periodic coefficients is studied and some sufficient conditions are presented for the existence of stabilizing solution

state feedback control of systems with multiplicative noise via linear matrix inequalities we consider lti systems perturbed by parametric uncertainties modeled as white noise disturbances we show how to maximize via state feedback control the smallest norm of the noise intensity vector producing instability in the mean square sense using convex optimization over linear matrix inequalities we also show how to maximize performance robustness where performance is measured by expected output energy with either bounded initial conditions and zero inputs classical lqg cost or zero initial conditions and deterministic inputs of bounded energy a generalization of the h norm

h2 optimal control for linear stochastic systems the aim of the present paper is to provide an optimal solution to the h 2 state feedback and output feedback control problems for stochastic linear systems subjected both to markov jumps and to multiplicative white noise it is proved that in the state feedback case the optimal solution is a static gain which is also optimal in the class of all higher order controllers in the output feedback case the optimal h 2 controller has the same order as the given stochastic system the realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of riccati type coupled equations an effective iterative convergent algorithm to compute these stabilizing solutions is also presented the paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature

linear quadratic control with stability degree constraint abstract the problem of static state feedback linear quadratic lq optimal control subject to a prescribed degree of stability for the closed loop system is considered in this paper a necessary optimality condition is given via the lagrange multiplier method a globally convergent algorithm is provided to solve the optimization problem it is shown that the algorithm recovers the standard lq feedback gain provided the desired stability degree is small enough to be within the range by the standard lq design as for other cases the optimum occurs on the boundary of the region a numerical example shows that the proposed algorithm provides a better design compared to the existing methods

finite time stabilizability detectability and dynamic output feedback finite time stabilization of linear systems in this note we deal with linear systems and we extend to the finite time setting the concepts of stabilizability and detectability it will be shown that similarly to what happens in the classical lyapunov framework even in the finite time context stabilizability and detectability play a role into the existence of stabilizing dynamical controllers we prove that a dynamic output feedback controller which finite time stabilizes the overall closed loop system exists if and only if the open loop system is finite time detectable and stabilizable plus a further linear matrix inequality coupling condition we also show that in the finite time context the equivalence between stabilizability via output feedback and stabilizability via observer based controllers is no longer true

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

control under stochastic multiplicative uncertainties part ii optimal design for performance this paper studies the optimal control design problem for linear discrete time systems with stochastic multiplicative uncertainties these uncertainties are assumed to be present in the control inputs and modeled as independent and identically distributed i i d random processes the optimal performance under study is defined in the mean square sense referred to as the mean square optimal h 2 performance it is shown that the mean square optimal h 2 control problem via state feedback can be solved using a mean square stabilizing solution to a modified algebraic riccati equation mare a necessary and sufficient condition for the existence of this solution is presented which constitutes a generalization of the solution to the classic optimal h 2 state feedback design problem whereas the latter can be obtained by solving an algebraic riccati equation are it is also proven that the optimal control design problem can be cast as an eigenvalue problem evp for the output feedback case with possible input delays we show that the mean square optimal h 2 control problem also amounts to solving an mare when the plant has no nonminimum phase zeros from the inputs to the measurement outputs that is the global optimal solution is obtained by solving an mare incorporating the delays the implication is that in this case a separation principle still holds

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

observability and detectability of discrete time stochastic systems with markovian jump abstract this paper studies detectability and observability of markov jump discrete time linear stochastic systems with multiplicative noise mjdls for short the relations between some concepts of detectability and observability are established these relations together with equivalent expressions of observability gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability as applications discrete time stochastic lyapunov equations and stochastic discrete algebraic riccati equations sdare are discussed

pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized h representation abstract the problem of pth moment asymptotic interval stability and stabilization for linear stochastic systems is investigated in this paper firstly we define the generalized h representation which is very helpful to transform stochastic systems into deterministic systems then the problems of pth moment interval stability the decay rate of state response and the estimation of pth moment lyapunov exponent are proposed with the help of the model transformation method furthermore the criteria for pth moment interval stabilization of the linear stochastic systems are addressed some necessary numerical examples are also provided to show the effectiveness of the addressed method

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

on the solutions of the first boundary value problem for the linear parabolic equations on etudie le premier probleme aux valeurs limites pour une equation parabolique lineaire d ordre 2 sous l hypothese que le terme inhomogene est continu en espace et en temps et continu de holder seulement par rapport aux variables d espace

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

a second order finite difference method for option pricing under jump diffusion models we develop a finite difference method to solve partial integro differential equations which describe the behavior of option prices under jump diffusion models with localization to a bounded domain of the spatial variable these equations are discretized on uniform grid points over a finite domain of time and spatial variables the proposed method is based on three time levels and leads to linear systems with tridiagonal matrices in this paper the stability of the proposed method and the second order convergence rate with respect to a discrete ell 2 norm are proved numerical results obtained with european put options under the merton and kou models show the behaviors of the stability and the second order convergence rate

absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty this paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty the uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints it is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system for each initial state of the system this controller can be found by parametric optimization of solutions of a parameter dependent generalized matrix riccati equation arising in stochastic h infty theory

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

a unified filter for simultaneous input and state estimation of linear discrete time stochastic systems in this paper we present a unified optimal and exponentially stable filter for linear discrete time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum variance sense without making any assumptions on the direct feedthrough matrix we also provide the connection between the stability of the estimator and a system property known as strong detectability and discuss the global optimality of the proposed filter finally an illustrative example is given to demonstrate the performance of the unified unbiased minimum variance filter

consensus seeking in multi agent systems with multiplicative measurement noises abstract in this paper the consensus problems of the continuous time integrator systems under noisy measurements are considered the measurement noises which appear when agents measure their neighbors states are modeled to be multiplicative by multiplication of the noises here the noise intensities are proportional to the absolute value of the relative states of an agent and its neighbor by using known distributed protocols for integrator agent systems the closed loop system is described in the vector form by a singular stochastic differential equation for the fixed and switching network topology cases constant consensus gains are properly selected such that mean square consensus and strong consensus can be achieved especially exponential mean square convergence of agents states to the common value is derived for the fixed topology case in addition asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied simulations shed light on the effectiveness of the proposed theoretical results

detectability observability and lyapunov type theorems of linear discrete time varying stochastic systems with multiplicative noise abstractthe objective of this paper is to study detectability observability and related lyapunov type theorems of linear discrete time time varying stochastic systems with multiplicative noise some new concepts such as uniform detectability k exact detectability resp kwft exact detectability kft exact detectability kn exact detectability and k exact observability resp kwft exact detectability kft exact detectability kn exact detectability are introduced respectively and nice properties associated with uniform detectability exact detectability and exact observability are also obtained moreover some lyapunov type theorems associated with generalised lyapunov equations and exponential stability in mean square sense are presented under uniform detectability kn exact observability and kn exact detectability respectively

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

european option pricing under stochastic volatility jump diffusion models with transaction cost abstract in this paper we consider an underlying general stochastic volatility jump diffusion model option pricing under this general model with transaction costs will lead to handling with nonlinear partial integro differential equations here after pide in this case option replication in a discrete time framework with transaction costs and the non uniqueness option pricing in such incomplete market will be studied observing and introducing a traded proxy for the volatility in the modern market we acquire a nonlinear pide in the advent of transaction costs under appropriate regularity conditions the existence of the strong solution to this pricing problem has been proved the corresponding self financing and positions readjustment for pricing a portfolio will also be discussed in the end

a sufficient condition for invalidation of linear state space systems with uncertain time varying parameters the model validation problem for linear systems with time varying parameter uncertainty and additive disturbances is addressed the disturbance are modelled using the window norm which is a generalization of the l norm and is shown to be attractive for optimal control an approximation of the nonlinear operator from parameters to output is found based on the frechet derivative using this approximation a sufficient condition for invalidation of a process model is formulated as a linear feasibility problem in this condition an upper bound for the approximation error is included an overhead crane is used as an illustrative example to show that the model validation test is realistic to perform even with large data sets

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

optimal filtering for a class of linear ito stochastic systems the dichotomic case this paper focuses on the problem of optimal h2 filtering for a class of continuous time stochastic systems without assuming their exponential stability in the mean square sense indeed the stability assumption is relaxed and we assume instead that the lyapunov operator associated to the dynamical stochastic system is exponentially dichotomic the optimal solution of the considered optimization problem is expressed in terms of the unique solution of a suitable algebraic lyapunov equation and the stabilizing solution of a certain algebraic riccati equation

some remarks on stability of stochastic singular systems with state dependent noise this paper discusses the stability for stochastic singular systems with state dependent noise in both continuous time and discrete time cases firstly the condition for the existence and uniqueness of the solution to stochastic singular systems is given based on this condition the stochastic ito singular system is transformed into a deterministic standard singular system by means of h representation method secondly new sufficient conditions for the stability of systems considered are derived in terms of strict linear matrix inequalities finally an example is given to illustrate the effectiveness of the obtained theoretical results

on the detectability and observability of continuous stochastic markov jump linear systems abstract this paper is concerned with the detectability and observability of continuous linear stochastic systems subject to markov jump by introducing some operators we investigate the relationship between some different concepts of detectability and observability and obtain their sufficient and necessary conditions continuous time stochastic lyapunov equations and stochastic continuous algebraic riccati equations are also discussed to serve as analysis tools