the stochastic maximum principle in singular optimal control with recursive utilities abstract in this paper we consider stochastic recursive optimal control problem in which the control variable has two components with the first absolutely continuous and the second singular the control domain of the first component needs not to be convex by using a spike variation on the absolutely continuous part of the control and a convex perturbation on the singular one respectively we obtain a stochastic maximum principle of the optimal control also we give the relationship of the backward variational equation the adjoint equation and forward variational equation

first and second order necessary conditions for stochastic optimal controls abstract the main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach the control system is governed by a stochastic differential equation in which both drift and diffusion terms may contain the control variable and the set of controls is allowed to be nonconvex only one adjoint equation is introduced to derive the first order necessary condition while only two adjoint equations are needed to state the second order necessary conditions for stochastic optimal controls

pointwise second order necessary conditions for stochastic optimal controls part i the case of convex control constraint this paper is the first part of our series of work to establish pointwise second order necessary conditions for stochastic optimal controls in this part both drift and diffusion terms may contain the control variable but the control region is assumed to be convex under some assumptions in terms of the malliavin calculus we establish the desired necessary conditions for stochastic singular optimal controls in the classical sense

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

brief paper stochastic maximum principle in the mean field controls in buckdahn djehiche li and peng 2009 the authors obtained mean field backward stochastic differential equations bsdes in a natural way as a limit of some highly dimensional system of forward and backward sdes corresponding to a great number of particles or agents the objective of the present paper is to deepen the investigation of such mean field bsdes by studying their stochastic maximum principle this paper studies the stochastic maximum principle smp for mean field controls which is different from the classical ones this paper deduces an smp in integral form and it also gets under additional assumptions necessary conditions as well as sufficient conditions for the optimality of a control as an application this paper studies a linear quadratic stochastic control problem of mean field type

the maximum principle for partially observed optimal control problems of mean field fbsdes abstractthis paper is concerned with a partially observed optimal control problem described by mean field forward and backward stochastic differential equations moreover the control variable ente

a constrained control problem with degenerate coefficients and degenerate backward spdes with singular terminal condition we study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact the coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation bspde with singular terminal condition for this degenerate bspde we prove existence and uniqueness of a nonnegative solution our existence result requires a novel gradient estimate for degenerate bspdes

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

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

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

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

the maximum principles for stochastic recursive optimal control problems under partial information a maximum principle for partially observed stochastic recursive optimal control problems is obtained under the assumption that control domains are not necessarily convex and forward diffusion coefficients do not contain control variables such kind of recursive optimal control problems have wide applications in finance and economics such as recursive utility optimization and principal agent problems by virtue of a classical spike variational approach and a filtering technique the maximum principle is obtained and the related adjoint processes are characterized by the solutions of forward backward stochastic differential equations in finite dimensional spaces then our theoretical results are applied to study a partially observed linear quadratic recursive optimal control problem in addition for the case with initial and terminal state constraints the corresponding maximum principle is also obtained by using ekeland s variational principle

a stochastic maximum principle for systems with jumps with applications to finance abstract we consider a stochastic control problem with linear dynamics with jumps convex cost criterion and convex state constraint in which the control enters the drift the diffusion and the jump coefficients we allow these coefficients to be random and do not impose any l p bounds on the control we obtain a stochastic maximum principle for this model that provides both necessary and sufficient conditions of optimality this is the first version of the stochastic maximum principle that covers the consumption investment problem in which there are jumps in the price system

moderate deviations of minimum contrast estimators under contamination since statistical models are simplifications of reality it is important in estimation theory to study the behavior of estimators also under distributions slightly different from the proposed model in testing theory when dealing with test statistics where nuisance parameters are estimated knowledge of the behavior of the estimators of the nuisance parameters is needed under alternatives to evaluate the power in this paper the moderate deviation behavior of minimum contrast estimators is investigated not only under the supposed model but also under distributions close to the model a particular example is the multivariate maximum likelihood estimator determined within the proposed model the set up is quite general including for instance also discrete distributions the rate of convergence under alternatives is determined both when comparing the minimum contrast estimator with a natural parameter in the parameter space and when comparing it with the proposed true value in the parameter space it turns out that under the model the asymptotic optimality of the maximum likelihood estimator in the local sense continues to hold in the moderate deviation area

on the necessary conditions of optimal controls for stochastic partial differential equations this paper concerns optimal control of systems governed by stochastic partial differential equations in which drift and diffusion terms are second and first order differential operators respectively necessary conditions for an optimal control are derived for both nondegenerate and degenerate systems and all the coefficients appearing in the equations are allowed to depend on the control variables furthermore the results obtained in the paper can also be used to derive necessary conditions of optimality for partially observed diffusions with correlation between the signals and the observation noises

a linear quadratic optimal control problem of forward backward stochastic differential equations with partial information this paper studies a linear quadratic optimal control problem derived by forward backward stochastic differential equations where the drift coefficient of the observation equation is linear with respect to the state x and the observation noise is correlated with the state noise in the sense that the cross variation of the state and the observation is nonzero a backward separation approach is introduced combining it with variational method and stochastic filtering two optimality conditions and a feedback representation of optimal control are derived closed form optimal solutions are obtained in some particular cases as an application of the optimality conditions a generalized recursive utility problem from financial markets is solved explicitly

stochastic maximum principle for optimal control with multiple priors abstract the necessary condition is derived for optimal control with multiple priors which are mutually singular the tool we use is the theory of g expectation

second order taylor expansion for backward doubly stochastic control system we consider the second order taylor expansion for backward doubly stochastic control system the results are obtained under no restriction on the convexity of control domain moreover the control variable is allowed in the drift coefficient and the diffusion coefficient

well posedness of backward stochastic differential equations with general filtration abstract this paper is addressed to the well posedness of some linear and semilinear backward stochastic differential equations with general filtration without using the martingale representation theorem the point of our approach is to introduce a new notion of solution i e the transposition solution which coincides with the usual strong solution when the filtration is natural but it is more flexible for the case of general filtration than the existing notion of solutions a comparison theorem for transposition solutions and a pontryagin type stochastic maximum principle are also presented

design of frames against buckling using a rayleigh quotient approximation a rayleigh quotient approximation is applied to the design of structures while guarding against elastic instability it approximates buckling eigenvalues by separately estimating the modal strain energy due to the linear and geometric stiffness of the structure previously used during structural optimization for the fundamental natural eigenvalue the rayleigh quotient approximation is derived for the buckling design problem for the first time the critical buckling load is found by solving the eigenvalue problem that arises by considering the geometric nonlinearity of the deforming structure rayleigh s principle is used to justify the choice of intermediate design variables for approximating terms in the rayleigh quotient a truss model illustrates the importance of the design space chosen for approximating the modal strain energy a beamtcolumn two plane frames and a space frame are used to verify the formulation special attention is paid to difficult bimodal optima

doubly smoothed em algorithm for statistical inverse problems recent results on discretization effects in unfolding intensity function of an indirectly observed nonhomogeneous poisson process show that a critical feasibility condition for the strong l2 consistency of the histogram sieve maximum likelihood estimates requires that the approximation error of the function of interest with step functions tend to 0 faster than the squared singular values of the discretized folding operator this condition may not be fulfilled in some standard inverse problems like for example the deconvolution problem and the wicksell problem discretized in a standard way the condition may be satisfied however with suitably modified discrete operator and suitably constructed parametric sets for the discrete problems motivated by these results an additional smoothing step is added to the ems expectation maximization smoothing algorithm and an automatic procedure for the choice of a smoothing parameter is proposed an application to the wicksell problem is presented in this contex

applicable stochastic control from theory to practice stochastic control has come of age it is currently applied in a wide variety of fields spanning cancer research and chemotherapy economics and finance engineering management and many other areas of scientific and social investigation both theoretical models formulated to elucidate some characteristics of a problem under study and practical applications which have sought to provide specific answers to well stated problems have been the subjects of intense research for example economists have simultaneously groped with the underlying theoretical constructs justifying the adoption of particular econometric models while at the same time attempting to devise algorithms and optimization approaches to provide economic policy guidelines based on these models in the same spirit t remendous interest in options management which are based on stochastic dynamic models has stimulated much research and numerical analyses not only in universities but also in the back rooms of trading firms the usefulness of stochastic control was recognized once it became clear that it can be used as a unifying framework for treating multi stage or multi period optimization problems subject to stochastic disturbances however just as it is convenient as a formalism to formulate such problems it is becoming increasingly clear that it is practically difficult to solve them there are in fact only few problems one can solve completely and obtain optimal solutions for this reason there is today an increased awareness that a broad range of techniques including stochastic approximations perturbation techniques markov decision processes etc are an essential part of stochastic control kits it is in such a spirit that computer software such as pandore of inria the adaptive control algorithms for econometric models developed by kendrick and many others has been devised providing thereby computer aided expertise for managing stochastic control problems this software is essential even after the great effort applied to solving such problems over the last three decades ever since bellman s principle of optimality there are very few non trivial problems we can solve theoretically these include the well known linear quadratic stochastic control scp problem some version of the multi armed bandit problem and some specific linear optimization problems for example even the adaptive control problems studied over the last few years by kendrick and his co workers and presumed to be convex are believed today to include some unspecified nonconvexities private communication by d kendrick and hans amman in this spirit the intent in this paper is to introduce salient aspects of stochastic control which are useful for applications in management a review of applications can be found in neck 1984 for example as well as in books such as tapiero 1977 1988 bensoussan hurst and naslund 1974 bensoussan kleindorfer and tapiero 1978 1980 sethi and thompson 1981 kamien and schwarz 1981 malliaris and brock 1982 and whittle 1982 further due to an awesome amount of research published in this area appearing under various connotations such a task has become unwieldy rather

martingale approach to stochastic differential games of control and stopping we develop a martingale approach for studying continuous time stochastic differential games of control and stopping in a non markovian framework and with the control affecting only the drift term of the state process under appropriate conditions we show that the game has a value and construct a saddle pair of optimal control and stopping strategies crucial in this construction is a characterization of saddle pairs in terms of pathwise and martingale properties of suitable quantities

on the cauchy problem for backward stochastic partial differential equations in holder spaces this paper is concerned with solution in holder spaces of the cauchy problem for linear and semi linear backward stochastic partial differential equations bspdes of super parabolic type the pair of unknown variables are viewed as deterministic spatial functionals which take values in banach spaces of random vector processes we define suitable functional holder spaces for them and give some inequalities among these holder norms the existence uniqueness as well as the regularity of solutions are proved for bspdes which contain new assertions even on deterministic pdes

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

minimum weight design of truss structures with geometric nonlinear behavior the paper presents an optimization method based on optimality criterion for minimum weight design of structures with geometric nonlinear behavior the nonlinear critical load is determined by finding the load level at which the hessian of the potential energy ceases to be positive definite a recurrence relation based on the criterion that at optimum the nonlinear strain energy density be equal in all the members is used to develop an algorithm sample problems are given to illustrate the application of the method to truss type structures with a large number of design variables number of algorithms based on the optimality criterion approach have been developed to design a minimum weight structure with specified constraints on nodal displacements element stresses system stability etc 1 2 the optimization algorithm consisted of analyzing the structure by the finite element method and using a recurrence relation derived from the appropriate optimality criterion to modify the design variables the optimality criterion was derived by differentiating the lagrangian with respect to the design variables the displacements were assumed to be small and in the finite element analysis linear equilibrium equations were solved to determine the response of the structure to the ap plied loads in the case of system stability the constraints were defined see refs 3 6 by the associated linear eigenvalue problem this definition of system stability for some structures may not be valid because of the nonlinear behavior of the structure which may be due to the geometry of the structure or the presence of geometric imperfections the correct procedure for these structures would be to analyze the structure by using nonlinear equilibrium equations this will be particularly true for large space structures lss in this paper an optimization method based on the optimality criterion approach is presented for structures with geometric nonlinear behavior in the case of a structure optimized with constraints on linear stability the optimum structure can have more than one critical buckling mode this design tends to become im perfection sensitive and a small deviation in the geometry of the structure can reduce its load carrying capacity sub stantially the imperfection sensitivity of the optimized structure can be reduced by designing the structure so that buckling loads associated with the critical buckling modes are not equal see ref 7 a real structure has geometric im perfections and these structures tend to have nonlinear

wm p solution p 2 of linear degenerate backward stochastic partial differential equations in the whole space abstract in this paper we consider the backward cauchy problem of linear degenerate stochastic partial differential equations we obtain the existence and uniqueness results in sobolev space l p c 0 t w m p with both m 1 and p 2 being arbitrary without imposing the symmetry condition for the coefficient of the gradient of the second unknown which was introduced by ma and yong 1999 21 in the case of p 2 to illustrate the application we give a maximum principle for optimal control of degenerate stochastic partial differential equations

partial information linear quadratic control for jump diffusions we study a stochastic control problem in which the state process is described by a stochastic differential equation sde that is driven by a brownian motion and a poisson random measure and is affine in both the state and the control the performance functional is quadratic in the state and the control all the coefficients are allowed to be random and non markovian moreover we may allow the control to be predictable to a given subfiltration of the filtration of the brownian motion and the random measure partial information control

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

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

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

backward stochastic partial differential equations with quadratic growth abstract this paper is concerned with the weak solution in analytic sense to the cauchy dirichlet problem of a backward stochastic partial differential equation when the nonhomogeneous term has a quadratic growth in both the gradient of the first unknown and the second unknown existence and uniqueness results are obtained under separate conditions

time inconsistent stochastic linear quadratic control in this paper we formulate a general time inconsistent stochastic linear quadratic lq control problem the time inconsistency arises from the presence of a quadratic term of the expected state as well as a state dependent term in the objective functional we define an equilibrium instead of optimal solution within the class of open loop controls and derive a sufficient condition for equilibrium controls via a flow of forward backward stochastic differential equations when the state is one dimensional and the coefficients in the problem are all deterministic we find an explicit equilibrium control as an application we then consider a mean variance portfolio selection model in a complete financial market where the risk free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes applying the general sufficient condition we obtain explicit equilibrium strategies when the risk premium is both deterministic and stochastic

maximum principle for forward backward sdes with a general cost functional abstractin this study we consider a stochastic optimal control problem whose state variables are described by the system of forward and backward stochastic differential equations with a general cost functional which relies on the global terminal condition in the framework of frechet derivatives we derive the corresponding maximum principle via constructing a series of adjoint equations which need to be solved step by step

backward stochastic differential equations with constraints on the gains process we consider backward stochastic differential equations with convex constraints on the gains or intensity of noise process existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is lipschitz continuous in the state and gains processes and convex in the gains process it is also shown that the minimal solution can be characterized as the unique solution of a functional stochastic control type equation this representation is related to the penalization method for constructing solutions of stochastic differential equations involves change of measure techniques and employs notions and results from convex analysis such as the support function of the convex set of constraints and its various properties

dynkin game of stochastic differential equations with random coefficients and associated backward stochastic partial differential variational inequality a dynkin game is considered for stochastic differential equations with random coefficients we first apply qiu and tang s maximum principle for backward stochastic partial differential equations to generalize a krylov estimate for the distribution of a markov process to that of a non markov process and establish a generalized ito kunita wentzell formula which allows the test function as an ito process to take values in a sobolev space we then prove the verification theorem that the nash equilibrium point and the value of the dynkin game are characterized by the strong solution of the associated hamilton jacobi bellman isaacs equation which is currently a backward stochastic partial differential variational inequality bspdvi with two obstacles finally we prove the existence and uniqueness result and a comparison theorem for strong solution of the bspdvi

general linear quadratic optimal stochastic control problems with random coefficients linear stochastic hamilton systems and backward stochastic riccati equations consider the minimization of the following quadratic cost functional j u e langle mx t x t rangle e int 0 t langle q sx s x s rangle langle n su s u s rangle ds where x is the solution of the following linear stochastic control system eq dx t a tx t b tu t dt sum i 1 d c t ix t d t iu t dw t i cr x 0 h cr u is a square integrable adapted process the problem is conventionally called the stochastic lq the abbreviation of linear quadratic problem we are concerned with the following general case the coefficients a b ci di q n and m are allowed to be adapted processes or random matrices we prove the existence and uniqueness result for the associated riccati equation which in our general case is a backward stochastic differential equation with the generator the drift term being highly nonlinear in the two unknown variables this solves bismut and peng s long standing open problem for the case of a brownian filtration which was initially proposed by the french mathematician j m bismut in seminaire de probabilites xii lecture notes in math 649 c dellacherie p a meyer and m weil eds springer verlag berlin 1978 pp 180 264 we also provide a rigorous derivation of the riccati equation from the stochastic hamilton system this completes the interrelationship between the riccati equation and the stochastic hamilton system as two different but equivalent tools for the stochastic lq problem there are two key points in our arguments the first one is to connect the existence of the solution of the riccati equation to the homomorphism of the stochastic flows derived from the optimally controlled system actually we establish their equivalence as a consequence we can construct solutions to a sequence of suitably modified riccati equations in terms of the associated stochastic hamilton systems and the optimal controls the second key point is to establish a new type of a priori estimate for solutions of riccati equations with which we show that the sequence of constructed solutions has a limit which is a solution to the original riccati 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

a minimum principle for stochastic control problems with output feedback a minimum principle for stochastic control problems with output feedback is derived by applying bismut s minimum principle for stochastic control problems with full information about the past to the kushner stratonovitch equation describing the controlled evolution of the conditional density of the state the well known solution of the linear quadratic gaussian problem is obtained from the principle

ϵ nash mean field games for linear quadratic systems with random jumps and applications this paper studies linear quadratic gaussian lqg games of stochastic large population system with jump diffusion processes the most distinguishing feature compared with the well studied mean fi

on the quasi linear reflected backward stochastic partial differential equations abstract this paper is concerned with the quasi linear reflected backward stochastic partial differential equation rbspde for short basing on the theory of backward stochastic partial differential equation and the parabolic capacity and potential we first associate rbspde to a variational problem and via the penalization method we prove the existence and uniqueness of the solution for linear rbspde with laplacian leading coefficients with the continuity approach we further obtain the well posedness of general quasi linear rbspdes related results including ito formulas for backward stochastic partial differential equations with stochastic regular measures the comparison principle for solutions of rbspdes and the connections with reflected backward stochastic differential equations and optimal stopping problems are addressed as well

the maximum principle for optimal control of diffusions with partial information we derive necessary conditions for the optimal control of a system that satisfies an ito equation with control entering the drift term the control is a function of a noise corrupted observation of the state and the cost is the expectation of an integral and a final term the robust form of the zakai equation from nonlinear filtering is used to compute the variation of the cost due to a strong or needle variation of a control this gives rise to an explicit formula for the adjoint process much as in the case with complete information

optimality conditions for stochastic boundary control problems governed by semilinear parabolic equations abstract we study the boundary control problems for stochastic parabolic equations with neumann boundary conditions imposing super parabolic conditions we establish the existence and uniqueness of the solution of state and adjoint equations with non homogeneous boundary conditions by the galerkin approximations method we also find that in this case the adjoint equation bspde has two boundary conditions one is non homogeneous the other is homogeneous by these results we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method

time inconsistent stochastic linear quadratic control characterization and uniqueness of equilibrium in this paper we continue our study on a general time inconsistent stochastic linear quadratic control problem originally formulated in y hu h jin and x y zhou siam j control optim 50 2012 pp 1548 1572 we derive a necessary and sufficient condition for equilibrium controls via a flow of forward backward stochastic differential equations when the state is one dimensional and the coefficients in the problem are all deterministic we prove that the explicit equilibrium control constructed in y hu h jin and x y zhou siam j control optim 50 2012 pp 1548 1572 is indeed unique our proof is based on the derived equivalent condition for equilibria as well as a stochastic version of the lebesgue differentiation theorem finally we show that the equilibrium strategy is unique for a mean variance portfolio selection model in a complete financial market where the risk free rate is a deterministic function of time but all the other market parameters are possibly stochastic pro

the relaxed optimal control problem for mean field sdes systems and application the present study deals with a new approach of optimal control problems where the state equation is a mean field stochastic differential equation and the set of strict classical controls need not be convex and the diffusion coefficient depends on the term control our consideration is based on only one adjoint process and the necessary conditions as well as a sufficient condition for optimality in the form of a relaxed maximum principle are obtained with application to linear quadratic stochastic control problem with mean field type

l p solutions of multidimensional bsdes with weak monotonicity and general growth generators abstract in this paper we first establish the existence and uniqueness of l p p 1 solutions for multidimensional backward stochastic differential equations bsdes under a weak monotonicity condition together with a general growth condition in y for the generator g then we overview several conditions related closely to the weak monotonicity condition and compare them in an effective way finally we put forward and prove a stability theorem and a comparison theorem of l p p 1 solutions for this kind of bsdes

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

nonlinear analysis of optimized structure with constraints on systemstability an optimization algorithm based on an optimality criterion was used to design a minimum weight space truss with different constraint requirements on system stability the constraints were specified so that the eigenvalues associated with all the critical buckling modes are either equal or separated by a specified factor for the second case the critical buckling mode was preselected from all the possible critical modes the designs obtained for the various constraint conditions were analyzed with and without specified geometric imperfections using a nonlinear finite element program which accounts for geometric nonlinearity the results obtained for various designs were compared for their imperfection sensitivity

effectiveness of linear bifurcation analysis for predicting the nonlinear stability limits of structures as an effort to predict effectively the actual collapse load of a structure a series of numerical studies on the stability of shell structures are made the difference in formulation between the two types of linear buckling loads the classical and the fully linearized is first demonstrated their correlations with respect to the actual stability limit of the structure are compared and finally the two types of critical load approximations are obtained at various stages of a nonlinear analysis to study the pattern of convergence to the actual collapse load it is found that the fully linearized buckling analysis when combined with nonlinear analysis can serve as a useful tool for prediction of the stability limit of a structure while for most types of structures the approximation is within engineering accuracy the rate of convergence of the extrapolated critical load also gives some insight to the accuracy of the approximation

a duality analysis on stochastic partial differential equations abstract the duality equations of stochastic partial differential equations are solved in the sobolev space h m w 2 m r d and the h m norm estimates of the solutions are obtained as an application the h m norm estimates with negative m for the solutions of stochastic partial differential equations are derived

a maximum principle for optimal control of stochastic evolution equations a general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations the control variable and linear unbounded operators act in both drift and diffusion terms and the control set need not be convex

well posedness and regularity of backward stochastic volterra integral equations backward stochastic volterra integral equations bsvies for short are studied notion of adapted m solution is introduced well posedness of bsvies is established and some regularity results are proved for the adapted m solutions via malliavin calculus a pontryagin type maximum principle is presented for optimal controls of stochastic volterra integral equations

a maximum principle for fully coupled stochastic control systems of mean field type abstract the present paper considers an optimal control problem for fully coupled forward backward stochastic differential equations fbsdes of mean field type in the case of controlled diffusion coefficient moreover the control domain is not assumed to be convex by virtue of a reduction method we establish the necessary optimality conditions of pontryagin s type as an application a linear quadratic stochastic control problem is studied

strong solution of backward stochastic partial differential equations in c 2 domains this paper is concerned with the strong solution to the cauchy dirichlet problem for backward stochastic partial differential equations of parabolic type existence and uniqueness theorems are obtained due to an application of the continuation method under fairly weak conditions on variable coefficients and c2 domains the problem is also considered in weighted sobolev spaces which allow the derivatives of the solutions to blow up near the boundary as applications a comparison theorem is obtained and the semi linear equation is discussed in the c2 domain

maximum principle for quasi linear backward stochastic partial differential equations abstract in this paper we are concerned with the maximum principle for quasi linear backward stochastic partial differential equations bspdes for short of parabolic type we first prove the existence and uniqueness of the weak solution to quasi linear bspdes with the null dirichlet condition on the lateral boundary then using the de giorgi iteration scheme we establish the maximum estimates and the global maximum principle for quasi linear bspdes to study the local regularity of weak solutions we also prove a local maximum principle for the backward stochastic parabolic de giorgi class

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

convergence of numerical solutions to stochastic age structured system of three species abstract in general most of stochastic age structured system of three species do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age structured system of three species

the maximum principle for partially observed optimal control of stochastic differential equations this paper concerns partially observed optimal control of possibly degenerate stochastic differential equations with correlated noises between the system and the observation the control is allowed to enter into all the coefficients a general maximum principle is proved for the partially observed optimal control and the relations among the adjoint processes are established adjoint vector fields which are adapted to the past and present observations are introduced as the solutions to some backward stochastic partial differential equations bspdes and their relations are established under suitable conditions the adjoint processes are characterized in terms of the adjoint vector fields their differentials and hessians along the optimal state process some other formulations of the partially observed stochastic maximum principle are then derived

structural design optimization of shallow frame structures undergoing large deflections an optimization algorithm for structural design against instability is developed for shallow beam structures undergoing large deflections the algorithm is based on the maximization of the limit load under specified volume constraint the analysis for obtaining the limit load involves coupling of axial and bending deformations and is based on the nonlinear finite element analysis using the displacement control technique the optimization is carried out using both the sequential quadratic programming sqp and optimality criterion oc techniques and the results are compared for the sqp technique the sensitivity derivatives of the critical load factor are calculated using the adjoint method based on the information obtained from the nonlinear buckling analysis a shallow plane arch illustrates the structural design optimization methodology and the results are compared with those in the literature it is shown that a design based on the generalized eigenvalue problem linear buckling gives an optimum limit load less than the initial limit load whereas the optimization using the nonlinear buckling analysis obtains a larger value for the optimum limit load compared to the initial limit load it has also been demonstrated that the optimum results obtained using oc technique are in good agreement with those obtained through sqp technique however the computational time for the oc is significantly lower than that of sqp which requires search techniques and sensitivity of the limit load for its successful completion and termination

optimality conditions for partial information stochastic control problems driven by levy processes abstract in this paper we consider a partial information stochastic control problem where the system is governed by a nonlinear stochastic differential equation driven by teugels martingales associated with some levy process and an independent brownian motion we prove optimality necessary conditions in the form of a maximum principle these conditions turn out to be sufficient under some convexity assumptions to illustrate the general results an example is solved

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

stochastic maximum principle for mean field type optimal control under partial information this technical note is concerned with a partially observed optimal control problem whose novel feature is that the cost functional is of mean field type hence determining the optimal control is time inconsistent in the sense that bellman s dynamic programming principle does not hold a maximum principle is established using girsanov s theorem and convex variation some nonlinear filtering results for backward stochastic differential equations bsdes are developed by expressing the solutions of the bsdes as some ito s processes an illustrative example is demonstrated in terms of the maximum principle and the filtering

the partially observed stochastic minimum principle using stochastic flows and the generalized differentiation formula of bismut and kunita the change in cost due to a strong variation of an optimal control is explicitly calculated differentiating this expression gives a minimum principle in both the partially observed and stochastic open loop situations in the latter case the equation satisfied by the adjoint process is obtained by applying a martingale representation result

design sensitivity analysis of non linear structures in regular and critical states abstract a general design sensitivity formulation is introduced for non linear elastic structures reaching critical equilibrium states a discretized formulation is considered first and the sensitivity analysis is discussed for regular and critical states including analysis of post critical behavior next a variational approach is presented for beam and surface structures for which generalized stress and strain operator formulation is applied the formulae for sensitivity of bifurcation loads are derived in terms of adjoint fields which are shown to be equivalent to post buckling fields in the case of symmetric bifurcation

structural design optimization of nonlinear symmetric structures using the group theoretic approach among multidisciplinary analysis and optimization problems structural optimization of geometrically nonlinear stability problems is of great importance especially in structures used in space applications because of their long and slender configurations in this study application of the group theoretic approach gta in structural optimization of geometrical nonlinear problems under system stability constraint has been investigated according to gta the number of displacement degrees of freedom in the initial configuration can be reduced significantly by using the set of symmetry transformations of the undeformed structure to construct a projection matrix from full space to a reduced subspace spanned by the symmetry modes a structural optimization algorithm is developed for shallow structures undergoing large deflections subject to system stability constraint the method combines the nonlinear buckling analysis based on the displacement control technique using gta with the optimality criteria approach based on the potential energy of the system a shallow dome truss structure has been designed to illustrate the proposed methodology this paper demonstrates that structural optimization of nonlinear symmetric structures using gta is computationally efficient and excellent agreement exists between optimal results in full space and those in the reduced subspace also it is shown that structural design based on the generalized eigenvalue problem linear buckling highly underestimates the optimum mass which may lead to structural failure