a maximum principle for fully coupled forward backward stochastic control systems with terminal state constraints abstract we study a stochastic optimal control problem where the controlled system is described by a fully coupled forward backward stochastic differential equation fbsde while the forward state is constrained in a convex set at the terminal time by introducing an equivalent backward control problem we use terminal variation approach to obtain a stochastic maximum principle applications to the utility optimization problem in the financial market and state constrained stochastic linear quadratic control models are investigated

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

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

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 control of backward stochastic differential equations this paper is concerned with optimal control of linear backward stochastic differential equations bsdes with a quadratic cost criteria or backward linear quadratic blq control the solution of this problem is obtained completely and explicitly by using an approach which is based primarily on the completion of squares technique two alternative though equivalent expressions for the optimal control are obtained the first of these involves a pair of riccati type equations an uncontrolled bsde and an uncontrolled forward stochastic differential equation sde while the second is in terms of a hamiltonian system contrary to the deterministic or stochastic forward case the optimal control is no longer a feedback of the current state rather it is a feedback of the entire history of the state a key step in our derivation is a proof of global solvability of the aforementioned riccati equations although of independent interest this issue has particular relevance to the blq problem since these riccati equations play a central role in our solution last but not least it is demonstrated that the optimal control obtained coincides with the solution of a certain forward linear quadratic lq problem this in turn reveals the origin of the riccati equations introduced

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

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

stability of discrete linear inclusion let m ai be a set of linear operators on rn the discrete linear inclusion dli m is the set of possible trajectories xi i 0 such that xn ainain 1 ai1x0 where x0 rn and aij m we study several notions of stability for dli m including absolute asymptotic stability aas which is that all products ain ai1 0 as n we mainly study the case that m is a finite set we give criteria for the various forms of stability two new approaches are taken one relates the question of aas of dli m to formal language theory and finite automata while the second connects the aas property to the structure of a lie algebra associated to the elements of m more generally the discrete linear inclusion dli m makes sense for m contained in a banach algebra b we prove some results for aas in this case and give counterexamples showing that some results valid for finite sets of operators on rn are not true for finite sets m in a general banach algebras b

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

finding adapted solutions of forward backward stochastic differential equations method of continuation the notion of bridge is introduced for systems of coupled forward backward stochastic differential equations fbsdes for short this notion helps us to unify the method of continuation in finding adapted solutions to such fbsdes over any finite time durations it is proved that if two fbsdes are linked by a bridge then they have the same unique solvability consequently by constructing appropriate bridges we obtain several classes of uniquely solvable fbsdes

wellposedness of mean field games with common noise under a weak monotonicity condition in this paper we consider mean field games in the presence of common noise relaxing the usual independence assumption of individual random noise we assume a simple linear model with terminal cost satisfying a convexity and a weak monotonicity property our main result is showing existence and uniqueness of a mean field game solution using the stochastic maximum principle the uniqueness is a result of a monotonicity property similar to that of lasry and lions we use the banach fixed point theorem to establish an existence over a small time duration and show that it can be extended over an arbitrary finite time duration

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

structural bias in population based algorithms challenging optimisation problems are abundant in all areas of science and industry since the 1950s scientists have responded to this by developing ever diversifying families of black box optimisation algorithms the latter are designed to be able to address any optimisation problem requiring only that the quality of any candidate solution can be calculated via a fitness function specific to the problem for such algorithms to be successful at least three properties are required i an effective informed sampling strategy that guides the generation of new candidates on the basis of the fitnesses and locations of previously visited candidates ii mechanisms to ensure efficiency so that for example the same candidates are not repeatedly visited and iii the absence of structural bias which if present would predispose the algorithm towards limiting its search to specific regions of the solution space the first two of these properties have been extensively investigated however the third is little understood and rarely explored in this article we provide theoretical and empirical analyses that contribute to the understanding of structural bias in particular we state and prove a theorem concerning the dynamics of population variance in the case of real valued search spaces and a flat fitness landscape this reveals how structural bias can arise and manifest as non uniform clustering of the population over time critically theory predicts that structural bias is exacerbated with independently increasing population size and increasing problem difficulty these predictions supported by our empirical analyses reveal two previously unrecognised aspects of structural bias that would seem vital for algorithm designers and practitioners respectively i increasing the population size though ostensibly promoting diversity will magnify any inherent structural bias and ii the effects of structural bias are more apparent when faced with many classes of difficult problems our theoretical result also contributes to the exploitation exploration conundrum in optimisation algorithm design by suggesting that two commonly used approaches to enhancing exploration increasing the population size and increasing the disruptiveness of search operators have quite distinct implications in terms of structural bias

solution of forward backward stochastic differential equations in this paper we study the existence and uniqueness of the solution to forward backward stochastic differential equations without the nondegeneracy condition for the forward equation under a certain monotonicity condition we prove the existence and uniqueness of the solution to forward backward stochastic differential equations

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

dynamic programming principle for one kind of stochastic recursive optimal control problem and hamilton jacobi bellman equation in this paper we study one kind of stochastic recursive optimal control problem with the obstacle constraint for the cost functional described by the solution of a reflected backward stochastic differential equation we give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding hamilton jacobi bellman equation

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

dynamic programming and pricing of contingent claims in an incomplete market the problem of pricing contingent claims or options from the price dynamics of certain securities is well understood in the context of a complete financial market this paper studies the same problem in an incomplete market when the market is incomplete prices cannot be derived from the absence of arbitrage since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolio of the basic securities in this situation there is a price range for the actual market price of the contingent claim the maximum and minimum prices are studied using stochastic control methods the main result of this work is the determination that the maximum price is the smallest price that allows the seller to hedge completely by a controlled portfolio of the basic securities a similar result is obtained for the minimum price which corresponds to the purchase price

efficiency of estimating equations and the use of pivots summary methods are proposed for deriving unbiased estimating equations for the parameters of interest in a statistical model which includes further incidental or nuisance parameters we start with pivot like quantities which eliminate the dependence on the incidental parameters and derive functions of these which give estimating equations which are most efficient in a certain sense these equations involve the incidental parameters which are then replaced by estimators the methods overcome some of the difficulties encountered in likelihood and least squares estimation when there are many incidental parameters and our theory reduces to likelihood and least squares estimation when there are none thus the optimality results apply to these methods too some examples are discussed

stochastic optimal control for backward stochastic partial differential systems abstract this paper studies optimal controls for a class of backward stochastic partial differential systems in the abstract evolution form under the assumption of a convex control domain necessary and sufficient conditions for an admissible control to be optimal are derived in the form of stochastic maximum principles by means of a convex variation method and a duality technique as an application the optimal control for a linear backward stochastic evolution equation bsee with quadratic cost criteria called bseelq problem is discussed and the corresponding optimal control is characterized via the stochastic hamilton system which is a linear full coupled forward backward stochastic evolution equation fbsee and consists of the state equation the adjoint equation and the dual presentation of the optimal control

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

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

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

corrigendum addendum to sets of matrices all infinite products of which converge abstract this corrigendum addendum supplies corrected statements and proofs of some results in our paper appearing in linear algebra appl 161 1992 227 263 these results concern special kinds of bounded semigroups of matrices it also reports on progress on the topics of this paper made in the last eight years

forward backward stochastic differential equations and quasilinear parabolic pdes this paper studies under some natural monotonicity conditions the theory existence and uniqueness a priori estimate continuous dependence on a parameter of forward backward stochastic differential equations and their connection with quasilinear parabolic partial differential equations we use a purely probabilistic approach and allow the forward equation to be degenerate

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

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

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

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

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

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

the generalized spectral radius and extremal norms the generalized spectral radius also known under the name of joint spectral radius or after taking logarithms maximal lyapunov exponent of a discrete inclusion is examined we present a new proof for a result of barabanov which states that for irreducible sets of matrices an extremal norm always exists this approach lends itself easily to the analysis of further properties of the generalized spectral radius we prove that the generalized spectral radius is locally lipschitz continuous on the space of compact irreducible sets of matrices and show a strict monotonicity property of the generalized spectral radius sufficient conditions for the existence of extremal norms are obtained

a leader follower stochastic linear quadratic differential game a leader follower stochastic differential game is considered with the state equation being a linear ito type stochastic differential equation and the cost functionals being quadratic we allow that the coefficients of the system and those of the cost functionals are random the controls enter the diffusion of the state equation and the weight matrices for the controls in the cost functionals are not necessarily positive definite the so called open loop strategies are considered only thus the follower first solves a stochastic linear quadratic lq optimal control problem with the aid of a stochastic riccati equation then the leader turns to solve a stochastic lq problem for a forward backward stochastic differential equation if such an lq problem is solvable one obtains an open loop solution to the two person leader follower stochastic differential game moreover it is shown that the open loop solution admits a state feedback representation if a new stochastic riccati equation is solvable

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

stability and paracontractivity of discrete linear inclusions abstract we study stability properties of a finite set of n n matrices such as paracontractivity bv and left convergent products lcps stability and their relations to each other the conjecture on equivalence of paracontractivity and lcp stability is proved moreover we prove the equivalence of the uniform bv stability and the property of vanishing length of steps of any trajectory of

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

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 eigenvalue problem for linear and affine iterated function systems abstract the eigenvalue problem for a linear function l centers on solving the eigen equation lx x this paper generalizes the eigenvalue problem from a single linear function to an iterated function system f consisting of possibly an infinite number of linear or affine functions the eigen equation becomes f x x where 0 is real x is a compact set and f x f f f x the main result is that an irreducible linear iterated function system f has a unique eigenvalue equal to the joint spectral radius of the functions in f and a corresponding eigenset s that is centrally symmetric star shaped and full dimensional results of barabanov and of dranisnikov konyagin protasov on the joint spectral radius follow as corollaries

optimality variational principle for controlled forward backward stochastic differential equations with mixed initial terminal conditions an optimal control problem for general coupled forward backward stochastic differential equations fbsdes with mixed initial terminal conditions is considered the control domain is not assumed to be convex and the control appears in the diffusion coefficient of the forward equation necessary conditions of pontraygin s type for the optimal controls are derived by means of spike variation techniques

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

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

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

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

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

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

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

ultrastructural relationships and canonical variates analysis summary the estimation of a multivariate ultrastructural relationship which includes functional and structural relationships is achievable by a canonical variates analysis in the case where the variance matrices of the error vectors are arbitrary and unknown

on the singular risk sensitive stochastic maximum principle we consider a risk sensitive stochastic control problem of a nonlinear system in which the variable control has two components the first being absolutely continuous and the second is singular the

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

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

asymptotic height optimization for topical ifs tetris heaps and the finiteness conjecture given an iterated function system ifs of topical maps verifying some conditions we prove that the asymptotic height optimization problems are equivalent to finding the extrema of a continuous functional the average height on some compact space of measures we give general results to determine these extrema and then apply them to two concrete problems first we give a new proof of the theorem that the densest heaps of two tetris pieces are sturmian second we construct an explicit counterexample to the lagarias wang finiteness conjecture