nonlinear kolmogorov equations in infinite dimensional spaces the backward stochastic differential equations approach and applications to optimal control solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control

necessary and sufficient conditions for near optimal harvesting control problem of stochastic age dependent system in this paper we consider a near optimal harvesting control problems for stochastic age structured population system we establish necessary and sufficient conditions for near optimality these conditions are described by adjoint equations and a nearly maximum condition on the hamiltonian the proof of the main result is based on ekeland s variational principle and the adjoint processes with respect to the control variable as is well known optimal controls may fail to exist even in simple cases this justifies the use of near optimal controls which exist under minimal assumptions and are sufficient in most practical cases at last an example is given for illustrating our results

h 2 h control for stochastic systems with delay this paper is concerned with the h2 h control problem for stochastic linear systems with delay in state control and external disturbance dependent noise a necessary and sufficient condition for the existence of a unique solution to the control problem is derived the resulting solution is characterised by a kind of complex generalised forward backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations especially we present the equivalent feedback solution via a new type of riccati equations to explain the theoretical results we apply them to a population control problem

on elements of prime power index in finite groups for an element x of a finite group g let indg x denote the index of cg x in g we prove that if ind a b x x is a prime power for any a b g then indg x is a prime power

deterministic near optimal controls part ii dynamic programming and viscosity solution approach near optimization is as sensible and important as optimization for both theory and applications this paper concerns dynamic near optimization or near optimal controls for systems governed by deterministic ordinary differential equations and uses dynamic programming to study the near optimality since nonsmoothness is inherent in this subject the viscosity solution approach is employed to investigate the problem the dynamic programming equation is derived in terms of e superdifferential subdifferential the relationships among the adjoint functions the value functions and the hamiltonian along near optimal trajectories are revealed verification theorems with which near optimal feedback controls can be constructed are obtained

linear quadratic optimal control for time delay stochastic system with recursive utility under full and partial information abstract this article studies a linear quadratic lq optimal control problem for time delay stochastic system with recursive utility under full and partial information the system is described by an anticipated forward backward stochastic delayed differential equation afbsdde we obtain an explicit representation of optimal control in an open loop form for the time delay problem by hamiltonian system which is an afbsdde in double dimensions d afbsdde also we study a partial information counterpart of the above problem and obtain an optimal control by optimal filtering as applications of theoretical results a cash management problem is solved analytic optimal controls are given and some figures are used to illustrate the influence of delay on optimal solution

optimal control of mean field jump diffusion systems with delay this paper is concerned with an optimal control problem under mean field jump diffusion systems with delay firstly some existence and uniqueness results are proved for a jump diffusion mean field stochastic delay differential equation and a jump diffusion mean field advanced backward stochastic differential equation then necessary and sufficient maximum principles for control systems of mean field type and with delay are established under certain conditions a mean field delayed linear quadratic control problem is finally discussed using the obtained maximum principles

near optimal control for stochastic recursive problems it is well documented e g zhou 1998 8 that the near optimal controls as the alternative to the exact optimal controls are of great importance for both the theoretical analysis and practical application purposes due to its nice structure and broad range availability feasibility as well as flexibility however the study of near optimality on the stochastic recursive problems to the best of our knowledge is a totally unexplored area thus we aim to fill this gap in this paper as the theoretical result a necessary condition as well as a sufficient condition of near optimality for stochastic recursive problems is derived by using ekeland s principle moreover we work out an e optimal control example to shed light on the application of the theoretical result our work develops that of 8 but in a rather different backward stochastic differential equation bsde context

brief paper maximum principle for the stochastic optimal control problem with delay and application in this paper we consider an optimal control problem for the stochastic system described by stochastic differential equations with delay we obtain the maximum principle for the optimal control of this problem by virtue of the duality method and the anticipated backward stochastic differential equations our results can be applied to a production and consumption choice problem the explicit optimal consumption rate is obtained

stochastic maximum principle for optimal control problems of forward backward systems involving impulse controls we consider a stochastic optimal control problem of a forward backward system in which the control variable consists of two components the continuous control and the impulse control the domain of the control is assumed to be convex necessary optimality conditions of the pontryagin maximum principle type are obtained for this stochastic optimal control problem we also give additional conditions under which the necessary optimality conditions turn out to be sufficient

a stochastic epidemic model with nonmonotone incidence rate sufficient and necessary conditions for near optimality abstract in this paper we studied the near optimal control of a stochastic susceptible infected recovered susceptible sirs model that includes a nonmonotone incidence rate the near optimal control problem was formulated by reducing the infected population while keeping the treatment cost to a minimum we obtained the sufficient and necessary conditions for the near optimality we showed that any near optimal control can be solved by using the hamiltonian function to approximate the cost function according to the adjoint equations we derived the estimate for the error bound of the near optimality numerical simulations were performed to illustrate the results and confirm the effect of treatment control on the disease dynamics

maximum principle for mean field jump diffusion stochastic delay differential equations and its application to finance abstract this paper investigates a stochastic optimal control problem with delay and of mean field type where the controlled state process is governed by a mean field jump diffusion stochastic delay differential equation two sufficient maximum principles and one necessary maximum principle are established for the underlying system as an application a bicriteria mean variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques under certain conditions explicit expressions are provided for the efficient portfolio and the efficient frontier which are as elegant as those in the classical mean variance problem without delays

maximum principle for nonzero sum stochastic differential game with delays in this technical note we discuss a nonzero sum stochastic differential game with delays not only the state variable but also control variables of players involve delays this kind of games are motivated by some interesting problems arising from economics and finance using anticipated backward stochastic differential equations we establish a necessary condition and a sufficient condition of maximum principle for the delayed game problem to explain theoretical results we apply them to an economic problem

on boundedly generated subgroups of profinite groups abstract in this paper we investigate the following general problem let g be a group and let i g be a property of g is there an integer d such that g contains a d generated subgroup h with i h i g here we consider the case where g is a profinite group and h is a closed subgroup extending earlier work of lucchini and others on finite groups for example we prove that d 3 if i g is the prime graph of g which is best possible and we show that d 2 if i g is the exponent of a finitely generated prosupersolvable group g

optimal consumption and portfolio with both fixed and proportional transaction costs we consider a market model with one risk free and one risky asset in which the dynamics of the risky asset are governed by a geometric brownian motion in this market we consider an investor who consumes from the bank account and who has the opportunity at any time to transfer funds between the two assets we suppose that these transfers involve a fixed transaction cost k 0 independent of the size of the transaction plus a cost proportional to the size of the transaction the objective is to maximize the cumulative expected utility of consumption over a planning horizon we formulate this problem as a combined stochastic control impulse control problem which in turn leads to a nonlinear quasi variational hamilton jacobi bellman inequality qvhjbi we prove that the value function is the unique viscosity solution of this qvhjbi finally numerical results are presented

stochastic maximum principle for delayed doubly stochastic control systems and their applications in this paper we investigate the optimal control problems for delayed doubly stochastic control systems we first discuss the existence and uniqueness of the delayed doubly stochastic differential

maximum principle for optimal control problems of forward backward regime switching system and applications abstract in this paper we derive the stochastic maximum principle for optimal control problems of the forward backward markovian regime switching system the control system is described by forward backward sdes and modulated by continuous time finite state markov chains we first obtain the necessary and sufficient conditions for the optimal control thereafter we apply the maximum principle to recursive utility investment consumption problems and lq problems with markovian regime switching

controllability of a quantum particle in a moving potential well we consider a nonrelativistic charged particle in a 1d moving potential well this quantum system is subject to a control which is the acceleration of the well it is represented by a wave function solution of a schrodinger equation the position of the well together with its velocity we prove the following controllability result for this bilinear control system given 0 close enough to an eigenstate and f close enough to another eigenstate the wave function can be moved exactly from 0 to f in finite time moreover we can control the position and the velocity of the well our proof uses moment theory a nash moser implicit function theorem the return method and expansion to the second order

growth of sobolev norms and controllability of the schrodinger equation in this paper we obtain a stabilization result for both linear and nonlinear schrodinger equations under generic assumptions on the potential then we consider the schrodinger equations with a potential which has a random time dependent amplitude we show that if the distribution of the amplitude is sufficiently non degenerate then any trajectory of the system is almost surely non bounded in sobolev spaces

technical communique a closed form optimal control for linear systems with equal state and input delays this paper presents the optimal regulator for a linear system with equal delays in state and input and a quadratic criterion the optimal regulator equations are obtained using the maximum principle performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulators available for the linear system without delays and for a rational approximation of the original time delay system simulation graphs demonstrating better performance of the obtained optimal regulator are included

a revisit to stochastic near optimal controls the critical case abstract this paper revisits the stochastic near optimal control problem considered in zhou 1998 where the stochastic system is given by a controlled stochastic differential equation with the control variable taking values in a general control space and entering both the drift and diffusion coefficients a necessary condition of near optimality is derived using ekeland s variational principle spike variation techniques and some delicate estimates for the state and the adjoint processes we improve the error bound of order from almost e 1 3 in zhou 1998 to exactly e 1 3

the relaxed general maximum principle for singular optimal control of diffusions in this paper we study optimality in stochastic control problems where the state process is a stochastic differential equation sde and the control variable has two components the first being abs

necessary and sufficient conditions for near optimality in stochastic control of fbsdes abstract we consider control problems for systems governed by a nonlinear forward backward stochastic differential equation fbsde we establish necessary as well as sufficient conditions for near optimality satisfied by all near optimal controls these conditions are described by two adjoint processes corresponding to the forward and backward components and a nearly maximum condition on the hamiltonian the proof of the main result is based on ekeland s variational principle and some estimates on the state and the adjoint processes with respect to the control variable as is well known optimal controls may fail to exist even in simple cases this justifies the use of near optimal controls which exist under minimal assumptions and are sufficient in most practical cases moreover since there are many nearly optimal controls it is possible to choose suitable ones that are convenient for implementation

brief paper near optimal control problems for linear forward backward stochastic systems herein we study the near optimality of linear forward backward stochastic control systems as the theoretical results some sufficient and necessary conditions of the near optimality are established in the form of pontryagin stochastic maximum principle as an illustration and practical application one e optimal control example is figured out and solved using our theoretical results

verification theorems within the framework of viscosity solutions abstract in optimal control theory the verification technique plays an important role in testing for the optimality of a given control and in constructing optimal feedback controls however the existing classical verification theorem is restrictive in that it requires the associated dynamic programming equation to have smooth solutions in this paper some verification theorems are presented within the framework of viscosity solutions under mild assumptions these theorems are shown to have wider applicability than the classical verification theorem as a relevant problem some differences and relationships between the viscosity solution and clarke s generalized gradient are also discussed

generalized solutions of the hamilton jacobi equation of stochastic control a second order generalized derivative based on brownian motion is introduced using this derivative an ito type formula is derived for functions f t x which are continuously differentiable in x with lipschitz derivative and are lipschitz continuous in t it is then shown that the value function of a stochastic control problem is a generalized solution of a second order hamilton jacobi equation such solutions are analogous to the clarke generalized solutions of first order hamilton jacobi equations finally it is shown that any generalized solution is a viscosity subsolution and a viscosity solution is a generalized solution

a combinatorial graph based solution method for a class of continuous time optimal control problems the paper addresses a class of continuous time optimal control problems whose solutions are typically characterized by both bang bang and singular control regimes analytical study and numerical computation of such solutions are very difficult and far from complete when only techniques from control theory are used this paper solves optimal control problems by reducing them to the combinatorial search for the shortest path in a specially constructed graph since the nodes of the graph are weighted in a sequence dependent manner we extend the classical shortest path algorithm to our case the proposed solution method is currently limited to single state problems with multiple control functions a production planning problem and a train operation problem are optimally solved to illustrate the method

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

constructive solution of a bilinear optimal control problem for a schrodinger equation abstract often considered in numerical simulations related to the control of quantum systems the so called monotonic schemes have not been so far much studied from the functional analysis point of view yet these procedures provide an efficient constructive method for solving a certain class of optimal control problems this paper aims both at extending the results already available about these algorithms in the finite dimensional case i e the time discretized case and at completing those of the continuous case this paper starts with some results about the regularity of a functional related to a wide class of models in quantum chemistry these enable us to extend an inequality due to ojasiewicz to the infinite dimensional case finally some inequalities proving the cauchy character of the monotonic sequence are obtained followed by an estimation of the rate of convergence

necessary conditions for optimal control of stochastic systems with random jumps a maximum principle is proved for optimal controls of stochastic systems with random jumps the control is allowed to enter into both diffusion and jump terms the form of the maximum principle turns out to be quite different from the one corresponding to the pure diffusion system the word pure here means the absence of the jump term in calculating the first order coefficient for the cost variation only a property for lebesgue integrals of scalar valued functions in the real number space cal r is used this shows that there is no essential difference between deterministic and stochastic systems as far as the derivation of maximum principles is concerned

optimality necessary conditions in singular stochastic control problems with nonsmooth data the present paper studies the stochastic maximum principle in singular optimal control where the state is governed by a stochastic differential equation with nonsmooth coefficients allowing both

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

stochastic controls with terminal contingent conditions abstract this paper considers a nonlinear stochastic control problem where the system dynamics is a controlled nonlinear backward stochastic differential equation and the state must coincide with a given random vector at the terminal time a necessary condition of optimality in the form of a global maximum principle as well as a sufficient condition of optimality are presented the general result is also applied to backward linear quadratic control problem and an optimal control is obtained explicitly as a feedback of the solution to a forward backward equation finally a nonlinear problem with additional integral constraints is discussed and it is shown that the duality gap is zero under the slater condition

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

a stochastic maximum principle for partially observed stochastic control systems with delay abstract this paper deals with partially observed optimal control problems for the state governed by stochastic differential equation with delay we develop a stochastic maximum principle for this kind of optimal control problems using a variational method and a filtering technique also we establish a sufficient condition without assumption of the concavity two examples that shed light on the theoretical results are established in the paper in particular in the example of an optimal investment problem with delay its numerical simulation shows the effect of delay via a discretization technique for forward backward stochastic differential equations fbsdes with delay and anticipate terms

the infinite time quadratic control problem for linear systems with state and control delays an evolution equation approach we show how a linear differential delay equation with delays in the control can be reformulated as an evolution equation with bounded input operator as a simple application we solve an infinite time quadratic cost control problem for the delay differential equation we also point out how our results even when specialized to the case where delays in the control disappear extend results previously published in the literature

some characterizations of optimal trajectories in control theory several characterizations of optimal trajectories for the classical mayer problem in optimal control are provided for this purpose the regularity of directional derivatives of the value function is studied for instance it is shown that for smooth control systems the value function v is continuously differentiable along an optimal trajectory x t 0 1 to bf r n provided v is differentiable at the initial point t 0 x t 0 then the upper semicontinuity of the optimal feedback map is deduced the problem of optimal design is addressed obtaining sufficient conditions for optimality finally it is shown that the optimal control problem may be reduced to a viability one

ito volterra optimal state estimation with continuous multirate randomly sampled and delayed measurements the optimal filter for continuous linear stochastic time varying systems described by the itocirc volterra equations with discontinuous measure is derived with an appropriately selected measure the result is applicable to a wide range of observation processes including the hybrid case of observations formed by an arbitrary combination of continuous and discrete measurements which may be sampled with a priori unknown changing and possibly random rates and delays the simultaneous presence of continuous and sampled measurements causes impulsive discontinuity in the inputs of the optimal filter equations which leads to a discontinuous change in state estimates every time a sampled measurement becomes available using the theory of vibrosolutions the explicit and unique expressions for the jumps in state estimates and estimation error covariance are derived several examples illustrate the procedure of modeling hybrid measurement systems by selecting an appropriate discontinuous measure we further show that the itocirc volterra model and the main result of the paper can be specialized to several important cases including state space systems for which we recover several known state estimation results and derive a novel optimal filter for continuous ltv systems with an arbitrary combination of continuous and delayed sampled measurements this optimal filter updates the state estimates for incoming measurements as soon as they become available and does not require prior knowledge of sampling instants and delays which makes it applicable when deterministic and random changes in sampling and delays are present several computational examples demonstrate the implementation of the developed filter and compare its performance to the traditional alternatives using monte carlo simulations

local exact controllability and stabilizability of the nonlinear schrodinger equation on a bounded interval this paper studies the exact controllability and the stabilization of the cubic schrodinger equation posed on a bounded interval both internal and boundary controls are considered and the results are given first in a periodic setting and next with dirichlet resp neumann boundary conditions it is shown that the systems with either an internal control or a boundary control are locally exactly controllable in the classical sobolev space h s for any s geq0 it is also shown that the systems with an internal stabilization are locally exponentially stabilizable in h s for any s geq0

necessary condition for near optimal control of linear forward backward stochastic differential equations this paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations where both the drift and diffusion terms are allowed to depend on controls and the control domain is not assumed to be convex in the previous work theorem 3 1 of the second and third authors some problem of near optimal control with the control dependent diffusion is addressed and our current paper can be viewed as some direct response to it the necessary condition of the near optimality is established within the framework of optimality variational principle developed by yong and obtained by the convergence technique to treat the optimal control of fbsdes in unbounded control domains by wu some new estimates are given here to handle the near optimality in addition an illustrating example is discussed as well

regularity for a schrodinger equation with singular potentials and application to bilinear optimal control abstract we study the schrodinger equation i t u u v 0 u v 1 u 0 on r 3 0 t where v 0 x t x a t 1 with a w 2 1 0 t r 3 is a coulombian potential singular at finite distance and v 1 is an electric potential possibly unbounded the initial condition u 0 h 2 r 3 is such that r 3 1 x 2 2 u 0 x 2 dx the potential v 1 is also real valued and may depend on space and time variables we prove that if v 1 is regular enough and at most quadratic at infinity this problem is well posed and the regularity of the initial data is conserved for the solution we also give an application to the bilinear optimal control of the solution through the electric potential

forward backward linear quadratic stochastic optimal control problem with delay abstract this paper is concerned with one kind of forward backward linear quadratic stochastic control problem whose system is described by a linear anticipated forward backward stochastic differential delayed equation the explicit form of the optimal control is derived optimal state feedback regulators are studied in two special cases for the case with delay in just the control variable the optimal state feedback regulator is obtained by the riccati equation for the other case with delay in just the state variable the optimal state feedback regulator is analyzed by the value function approach

necessary and sufficient conditions for near optimality of stochastic delay systems in this paper we study a class of near optimisation problems with controlled systems described by the stochastic differential equations with delay thanks to the ekeland s variational principle w

optimal bilinear control of nonlinear schrodinger equations with singular potentials abstract we consider an optimal bilinear control problem for the nonlinear schrodinger equations with singular potentials we show the well posedness of the problem and the existence of an optimal control in addition the first order optimality system is rigorously derived our results give an improvement for some recent results

linear quadratic regulation and stabilization of discrete time systems with delay and multiplicative noise this paper is concerned with the long standing problems of linear quadratic regulation lqr control and stabilization for a class of discrete time stochastic systems involving multiplicative noises and input delay these fundamental problems have attracted resurgent interests due to development of networked control systems an explicit analytical expression is given for the optimal lqr controller more specifically the optimal lqr controller is shown to be a linear function of the conditional expectation of the state with the feedback gain based on a riccati zxl difference equation it is also shown that the system is stabilizable in the mean square sense if and only if an algebraic riccati zxl equation has a particular solution these results are based on a new technical tool which establishes a non homogeneous relationship between the state and the costate of this class of systems and the introduction of a new lyapunov function for the finite horizon optimal control design

recognizing the prime divisors of the index of a proper subgroup abstract let g be a finite group and let c be a subgroup of g we prove that in order to get information on the set of primes dividing the index g c of c in g it is enough to look at the primes dividing h c h where h is a suitable subgroup of g with few generators

near optimal controls of random switching lq problems with indefinite control weight costs in this paper we consider hybrid controls for a class of linear quadratic problems with white noise perturbation and markov regime switching where the regime switching is modeled by a continuous time markov chain with a large state space and the control weights are indefinite the use of large state space enables us to take various factors of uncertain environment into consideration yet it creates computational overhead and adds difficulties aiming at reduction of complexity we demonstrate how to construct near optimal controls first in the model we introduce a small parameter to highlight the contrast of the weak and strong interactions and fast and slow motions this results in a two time scale formulation in view of the recent developments on lq problems with indefinite control weights and two time scale markov chains we then establish the convergence of the system of riccati equations associated with the hybrid lq problem based on the optimal feedback control of the limit system obtained using the system of riccati equations we construct controls for the original problem and show that such controls are near optimal a numerical demonstration of a simple system is presented here

existence and optimality conditions for relaxed mean field stochastic control problems abstract we consider optimal control problems for systems governed by mean field stochastic differential equations where the control enters both the drift and the diffusion coefficient we study the relaxed model in which admissible controls are measure valued processes and the relaxed state process is driven by an orthogonal martingale measure whose covariance measure is the relaxed control this is a natural extension of the original strict control problem for which we prove the existence of an optimal control then we derive optimality necessary conditions for this problem in terms of two adjoint processes extending the known results to the case of relaxed controls

optimal bilinear control of gross pitaevskii equations a mathematical framework for optimal bilinear control of nonlinear schrodinger equations of gross pitaevskii type arising in the description of bose einstein condensates is presented the obtained results generalize earlier efforts found in the literature in several aspects in particular the cost induced by the physical workload over the control process is taken into account rather than the often used l 2 or h 1 norms for the cost of the control action well posedness of the problem and existence of an optimal control are proved in addition the first order optimality system is rigorously derived also a numerical solution method is proposed which is based on a newton type iteration and used to solve several coherent quantum control problems

existence of optimal controls for systems driven by fbsdes abstract we prove the existence of optimal relaxed controls as well as strict optimal controls for systems governed by non linear forward backward stochastic differential equations fbsdes our approach is based on weak convergence techniques for the associated fbsdes in the jakubowski s topology and a suitable skorokhod representation theorem

a probabilistic approach to the generalized hessian the quadratic variation of brownian motion is used to give a new definition of a generalized hessian for nonsmooth functions totally independently of any gradients a calculus is developed for the generalized hessian of functions whose gradient is lipschitz it is also shown that for convex functions the hessian is nonempty

stochastic near optimal controls necessary and sufficient conditions for near optimality near optimization is as sensible and important as optimization for both theory and applications this paper concerns dynamic near optimization or near optimal controls for systems governed by the ito stochastic differential equations sdes where both the drift and diffusion terms are allowed to depend on controls and the systems are allowed to be degenerate necessary and sufficient conditions for a control to be near optimal are studied it is shown that any near optimal control nearly maximizes the hh function which is a generalization of the usual hamiltonian and is quadratic with respect to the diffusion coefficients in some integral sense and vice versa if certain additional concavity conditions are imposed error estimates for both the near optimality of the controls and the near maximum of the hh function are obtained based on some delicate estimates of the adjoint processes examples are presented to demonstrate the results

the stochastic maximum principle for linear convex optimal control with random coefficients this paper considers a stochastic control problem with linear dynamics convex cost criterion and convex state constraint in which the control enters both the drift and diffusion coefficients these coefficients are allowed to be random and no l p bounds are imposed on the control an explicit solution for the adjoint equation and a global stochastic maximum principle are obtained for this model this is evidently the first version of the stochastic maximum principle that covers the consumption investment problem the mathematical tools are those of stochastic calculus and convex analysis when it is assumed as in other versions of the stochastic maximum principle that the admissible controls are square integrable not only a necessary but also a sufficient condition for optimality is obtained it is then shown that this particular case of the general model may be applied to solve a variety of problems in stochastic control including the linear regulator predicted miss and benes problems

the relationship between the maximum principle and dynamic programming let v t x be the infimum cost of an optimal control problem viewed as a function of the initial time and state t x dynamic programming is concerned with the properties of v cdot cdot and in particular with its characterization as a solution to the hamilton jacobi bellman equation heuristic arguments have long been advanced relating the maximum principle to dynamic programming according to p t v x left t x 0 t right here x 0 cdot is the minimizing state function under consideration and p cdot is the costate function of the maximum principle in this paper we examine the validity of such claims and find that this relationship interpreted as a differential inclusion involving the generalized gradient is indeed true almost everywhere and at the endpoints for a very large class of nonsmooth optimal control problems

technical communique near optimal control for a class of stochastic hybrid systems to address a computationally intractable optimal control problem for a class of stochastic hybrid systems this paper proposes a near optimal state feedback control scheme which is constructed by using a statistical prediction method based on approximate numerical solution that samples over the entire state space a numerical example illustrates the potential of the approach

exact controllability for the schrodinger equation the exact controllability of schrodinger equation in bounded domains with dirichlet boundary condition is studied both the boundary controllability and the internal controllability problems are considered concerning the boundary controllability the paper proves the exact controllability in h 1 omega with l 2 boundary control on the other hand the exact controllability in l 2 omega is proved with l 2 controls supported in a neighborhood of the boundary both results hold for an arbitrarily small time the method of proof combines both the hum hilbert uniqueness method and multiplier techniques

fully coupled forward backward stochastic differential equations and applications to optimal control existence and uniqueness results of fully coupled forward backward stochastic differential equations with an arbitrarily large time duration are obtained some stochastic hamilton systems arising in stochastic optimal control systems and mathematical finance can be treated within our framework

the stochastic maximum principle for optimal control problems of delay systems involving continuous and impulse controls this paper is concerned with a pontryagin s maximum principle for stochastic optimal control problems of delay systems with random coefficients involving both continuous and impulse controls this kind of control problems is motivated by some interesting phenomena arising from economics and finance we establish a necessary maximum principle and a sufficient verification theorem by virtue of the duality and the convex analysis to explain the theoretical results we apply them to a production and consumption choice problem

anticipated backward stochastic differential equations in this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations anticipated bsdes in these equations the generator includes not only the values of solutions of the present but also the future we show that these anticipated bsdes have unique solutions a comparison theorem for their solutions and a duality between them and stochastic differential delay equations

exact boundary controllability of the nonlinear schrodinger equation abstract this paper studies the exact boundary controllability of the semi linear schrodinger equation posed on a bounded domain r n with either the dirichlet boundary conditions or the neumann boundary conditions it is shown that if s n 2 or 0 s n 2 with 1 n 2 2 s or s 0 1 with n 2 then the systems are locally exactly controllable in the classical sobolev space h s around any smooth solution of the cubic schrodinger equation

near optimality conditions in stochastic control of jump diffusion processes abstract this paper is concerned with necessary as well as sufficient conditions for near optimality of controlled jump diffusion processes necessary conditions for a control to be near optimal are derived using ekeland s variational principle and some stability results on the state and adjoint processes with respect to the control variable in a second step we show that the necessary conditions for near optimality are in fact sufficient for near optimality provided some concavity conditions are fulfilled finally as an illustration some examples are solved explicitly

the pontryagin maximum principle from dynamic programming and viscosity solutions to first order partial differential equations on demontre le principe de maximum de pontryagin pour le probleme de lagrange de commande optimale en utilisant le fait que la fonction valeur du probleme est la solution viscosite de l equation de hamilton jacobi bellman associee

a general maximum principle for optimal control of forward backward stochastic systems abstract a general maximum principle for optimal control problems derived by forward backward stochastic systems is established where control domains are non convex and forward diffusion coefficients explicitly depend on control variables these optimal control problems have broad applications in mathematical finance and economics such as the recursive mean variance portfolio choice problems the maximum principle is applied to study a forward backward linear quadratic optimal control problem with a non convex control domain an optimal solution is obtained

comparison theorems for anticipated bsdes with non lipschitz coefficients abstract we study comparison theorems for one dimensional anticipated backward stochastic differential equations under one kind of non lipschitz assumption in the results the generator functions are allowed to contain the anticipated term of z neither generator function needs to be necessarily monotone in the anticipated term of y and the anticipated times of the anticipated terms of y z in one generator function can differ from those in the other

a characterisation of f2 g in 1 we obtained a short proof of the theorem of thompson that a finite group is soluble if and only if every two of its elements generate a soluble subgroup a natural next question to ask is what happens if we keep one of the generators fixed for a finite group we define sol g the soluble radical of g to be the largest normal soluble subgroup of g and sol g x g x g is soluble for all g g

the risk sensitive maximum principle for controlled forward backward stochastic differential equations abstract in this paper we consider the risk sensitive optimal control problem for forward backward stochastic differential equations fbsdes we consider two different cases case 1 the drift and diffusion terms of the forward part are independent of the backward part not fully coupled fbsde and the running cost does not include the backward part case 2 the fully coupled fbsde with terminal and initial costs in both cases the risk sensitive objective functional is considered the corresponding control domain is not necessarily convex and the diffusion term of the forward part depends on control and state variables in both cases by using the nonlinear transformations of the equivalent risk neutral problems we obtain two different risk sensitive maximum principles which are characterized in terms of the variational inequalities we show that the risk sensitive maximum principle of case 1 consists of the two coupled adjoint equations with an additional scalar adjoint equation which are backward stochastic differential equations bsdes the risk sensitive maximum principle of case 2 consists of the two coupled adjoint equations which are coupled fbsdes with an additional scalar adjoint equation and optimality conditions in both cases the additional scalar adjoint equations are bsdes which are induced due to the nonlinear transformations of the adjoint processes in the equivalent risk neutral problems through the application of results we consider the linear quadratic risk sensitive optimal control problem for the linear fbsde and by using the risk sensitive maximum principle of case 1 we characterize an explicit optimal solution

optimal bilinear control of an abstract schro dinger equation well posedness of abstract quantum mechanical systems is considered and the existence of optimal control of such systems is proved first order optimality systems are derived convergence of the monotone scheme for the solution of the optimality system is proved

hamilton jacobi equations viscosity solutions and generalized gradients this paper is devoted to the relationship between locally lipschitz continuous viscosity solutions and solutions in the sense of clarke of the hamilton jacobi equation arising in optimal control

near maximum principle for general recursive utility optimal control problem in this study we introduce a general recursive utility optimal control problem driven by a fully nonlinear stochastic differential system in order to investigate pontryagin s stochastic maximum p

control for ito stochastic systems with input delay this paper examines the long standing problem of linear quadratic regulation and stabilization for ito stochastic systems with input delay this problem remains a primary challenge because the separation principle does not hold for ito stochastic systems this paper presents a complete solution to the problem 1 the sufficient and necessary solvability condition of the optimal control and the analytical controller are given based on the modified riccati differential equation defined herein 2 the sufficient and necessary stabilization condition in mean square sense is explored we show that the ito stochastic system with input delay is stabilized if and only if the modified algebraic riccati equation developed in this paper has a unique positive definite solution the essential obstacle encountered in this paper concerns a delayed forward backward stochastic differential equation d fbsde which is mathematical challenging

stochastic dynamic job shops and hierarchical production planning this paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products the concept of a dynamic job shop is introduced by interpreting the system as a directed graph and the structure of the system dynamics is characterized for its use in the asymptotic analysis the optimal control problem for the system is a state constrained problem since the number of parts in any buffer between any two machines must remain nonnegative a limiting problem is introduced in which the stochastic machine capacities are replaced by corresponding equilibrium mean capacities as the rate of change in machine states approaches infinity the value function of the original problem is shown to converge to that of the limiting problem and the convergence rate is obtained furthermore near optimal controls for the original problem are constructed from near optimal controls of the limiting problem and an error estimate is obtained on the near optimality of the constructed controls

maximum principle for singular stochastic control problems in this paper an optimal singular stochastic control problem is considered for this model a general stochastic maximum principle is obtained by using a time transformation this is the first version of the stochastic maximum principle that covers nonlinear cases

portfolio selection with transaction costs in this paper optimal consumption and investment decisions are studied for an investor who has available a bank account paying a fixed rate of interest and a stock whose price is a log normal diffusion this problem was solved by merton and others when transactions between bank and stock are costless here we suppose that there are charges on all transactions equal to a fixed percentage of the amount transacted it is shown that the optimal buying and selling policies are the local times of the two dimensional process of bank and stock holdings at the boundaries of a wedge shaped region which is determined by the solution of a nonlinear free boundary problem an algorithm for solving the free boundary problem is given

stochastic equations with delay optimal control via bsdes and regular solutions of hamilton jacobi bellman equations we consider an ito stochastic differential equation with delay driven by brownian motion whose solution by an appropriate reformulation defines a markov process x with values in a space of continuous functions mathbf c with generator mathcal l we then consider a backward stochastic differential equation depending on x with unknown processes y z and we study properties of the resulting system in particular we identify the process z as a deterministic functional of x we next prove that the forward backward system provides a suitable solution to a class of parabolic partial differential equations on the space mathbf c driven by mathcal l and we apply this result to prove a characterization of the fair price and the hedging strategy for a financial market with memory effects we also include applications to optimal stochastic control of differential equation with delay in particular we characterize optimal controls as feedback laws in terms of the process x

optimal filtering for linear state delay systems in this note the optimal filtering problem for linear systems with state delay over linear observations is treated proceeding from the general expression for the stochastic ito differential of the optimal estimate and the error variance as a result the optimal estimate equation similar to the traditional kalman bucy one is derived however it is impossible to obtain a system of the filtering equations that is closed with respect to the only two variables the optimal estimate and the error variance as in the kalman bucy filter the resulting system of equations for determining the error variance consists of a set of equations whose number is specified by the ratio between the current filtering horizon and the delay value in the state equation and increases as the filtering horizon tends to infinity in the example performance of the designed optimal filter for linear systems with state delay is verified against the best kalman bucy filter available for linear systems without delays and two versions of the extended kalman bucy filter for time delay systems