a test of static equilibrium models and rates of return to quasi fixed factors with an application to the bell system abstract the paper provides a statistical test to assess the adequacy of the static equilibrium framework which can be used prior to specifying a fully dynamic equilibrium model we develop and apply this test to the production structure and factor demand equations based on the theory of restricted cost functions this diagnostic test can also be used in other areas of applied economics such as consumer demand and labor supply studies where the analyst faces the choice between static and dynamic models of economic behavior the framework is used to calculate rates of return to quasi fixed factors to measure the extent of over and underinvestment in such factors to adjust measured productivity growth for departures from static equilibrium and to provide measures of marginal tobin s q for individual assets that could be used to model investment functions for those assets

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

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

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

probabilistic analysis of mean field games the purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games with mean field interactions we implement the mean field game strategy developed analytically by lasry and lions in a purely probabilistic framework relying on tailor made forms of the stochastic maximum principle while we assume that the state dynamics are affine in the states and the controls and the costs are convex our assumptions on the nature of the dependence of all the coefficients upon the statistical distribution of the states of the individual players remains of a rather general nature our probabilistic approach calls for the solution of systems of forward backward stochastic differential equations of a mckean vlasov type for which no existence result is known and for which we prove existence and regularity of the corresponding value function finally we prove that a solution of the mean field game problem as formulated by lasry and lions does indeed provide appr

tests on the validity of static equilibrium models abstract this paper provides a framework to test the validity of static cost minimizing equilibrium assumptions that form the basis for much of the empirical literature on industrial production the point of departure in our model is to allow the observed technology to be at a short run equilibrium where firms minimize variable costs while being constrained by the utilization levels of quasi fixed factors the long run equilibrium is then inferred by minimizing total costs with the optimal adjustment of quasi fixed factor levels we use results from the optimization problem to form tests with respect to quantities and prices in the quantity space version departures between the actual and the optimal long run levels of quasi fixed factors are tested for statistical significance a significant non zero departure implies the rejection of a static equilibrium specification in the price space version the test is cast as a comparison of the market price and the long run shadow value of a quasi fixed factor although the two versions would give identical results in the non stochastic case the rejection powers of these two tests are found to depend on the particular functional form chosen to represent the production process i e cost function in an application based on aggregate u s manufacturing where capital is taken to be quasi fixed we were able to reject the static equilibrium specification these results cast doubt on the validity of a number of previous empirical studies

the geometric structures and instability of entropic dynamical models in this paper we characterize two entropic dynamical ed models from the viewpoint of information geometry and give the geometric structures of the associated statistical manifolds of the models the scalar curvatures and the geodesics are obtained also the instability of entropic dynamical models is studied from the behavior of the geodesics lengths statistical volume elements and jacobi vector fields

optimal control under stochastic target constraints we study a class of markovian optimal stochastic control problems in which the controlled process z nu is constrained to satisfy an almost sure constraint z nu t in g subset mathbb r d 1 mathbb p a s at some final time t 0 when the set is of the form g x y in mathbb r d times mathbb r g x y geq0 with g nondecreasing in y we provide a hamilton jacobi bellman characterization of the associated value function it gives rise to a state constraint problem where the constraint can be expressed in terms of an auxiliary value function w which characterizes the set d t z nu t in 0 t times mathbb r d 1 z nu t in g a s for some nu contrary to standard state constraint problems the domain d is not given a priori and we do not need to impose conditions on its boundary it is naturally incorporated in the auxiliary value function w which itself is a viscosity solution of a nonlinear parabolic pde applying ideas recently developed in bouchard elie and touzi siam j control optim 48 2009 pp 3123 3150 our general result also allows us to consider optimal control problems with moment constraints of the form mathbb e g z nu t geq0 or mathbb p g z nu t geq0 geq p

state constrained stochastic optimal control problems via reachability approach this paper deals with a class of stochastic optimal control problems socps in the presence of state constraints it is well known that for such problems the value function is in general discontinuous and its characterization by a hamilton jacobi equation requires additional assumptions involving an interplay between the boundary of the set of constraints and the dynamics of the controlled system here we give a characterization of the epigraph of the value function without assuming the usual controllability assumptions to this end the socp is first translated into a state constrained stochastic target problem then a level set approach is used to describe the backward reachable sets of the new target problem it turns out that these backward reachable sets describe the value function the main advantage of our approach is that it allows us to easily handle the state constraints by an exact penalization however the target problem involves a new state variable and a new control variable that is u

optimal control problems of fully coupled fbsdes and viscosity solutions of hamilton jacobi bellman equations in this paper we study stochastic optimal control problems of fully coupled forward backward stochastic differential equations fbsdes the recursive cost functionals are defined by controlled fully coupled fbsdes we use a new method to prove that the value functions are deterministic satisfy the dynamic programming principle and are viscosity solutions to the associated generalized hamilton jacobi bellman hjb equations for this we generalize the notion of stochastic backward semigroup introduced by peng topics on stochastic analysis science press beijing 1997 pp 85 138 we emphasize that when sigma depends on the second component of the solution y z of the bsde it makes the stochastic control much more complicated and has as a consequence that the associated hjb equation is combined with an algebraic equation we prove that the algebraic equation has a unique solution and moreover we also give the representation for this solution on the other hand we prove a new local existence

jacobi fields on statistical manifolds of negative curvature abstract two entropic dynamical models are considered the geometric structure of the statistical manifolds underlying these models is studied it is found that in both cases the resulting metric manifolds are negatively curved moreover the geodesics on each manifold are described by hyperbolic trajectories a detailed analysis based on the jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability a comparison between the two models leads to a relation among statistical curvature stability of geodesics and relative entropy like quantities finally the jacobi vector field intensity and the entropy like quantity are suggested as possible indicators of chaoticity in the ed models due to their similarity to the conventional chaos indicators based on the riemannian geometric approach and the zurek paz criterion of linear entropy growth respectively

parametric tests for static and dynamic equilibrium econometric estimates of the characteristics of production are highly sensitive to the choice of dynamic specification in this paper we propose a new approach for testing whether inputs are in static equilibrium the procedure which is based on the use of a generalized cost function tests for divergences between the actual and static equilibrium quantities of all inputs simultaneously and symmetrically we apply it to two widely used data sets one at a high level of aggregation and the other at the firm level and strongly reject static equilibrium in both cases

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

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

risk sensitive zero sum differential games we consider two player risk sensitive zero sum differential games rszsdgs in our problem setup both the drift term and the diffusion term in the controlled stochastic differential equation are dependent on the state and controls of both players and the objective functional is of the risk sensitive type first a stochastic maximum principle type necessary condition for an open loop saddle point of the rszsdg is established via nonlinear transformations of the adjoint processes of the equivalent risk neutral stochastic zero sum differential game in particular we obtain two variational inequalities namely the pair of saddle point inequalities of the rszsdg next we obtain the hamilton jacobi isaacs partial differential equation for the rszsdg which provides a sufficient condition for a feedback saddle point of the rszsdg using a logarithmic transformation of the associated value function finally we study the extended linear quadratic rszsdg lq rszsdg we show intractability of the extended lq rszsdg with the state and or controls of both players appearing in the diffusion term this unexpected intractability could lead to nonlinear open loop and feedback saddle points even if the problem itself is essentially lq and the isaacs condition holds

information geometric characterization of the complexity of fractional brownian motions the complexity of the fractional brownian motions is investigated from the viewpoint of information geometry by introducing a riemannian metric on the space of their power spectral densities the geometric structure is achieved based on the general construction for an example whose power spectral density is obtained by use of the normalized mexican hat wavelet we show its information geometric structures e g the dual connections the curvatures and the geodesics furthermore the instability of the geodesic spreads on this manifold is analyzed via the behaviors of the length between two neighboring geodesics the average volume element as well as the divergence or instability of the jacobi vector field finally the lyapunov exponent is obtained

stochastic differential games and viscosity solutions of hamilton jacobi bellman isaacs equations in this paper we study zero sum two player stochastic differential games with the help of the theory of backward stochastic differential equations bsdes more precisely we generalize the results of the pioneering work of fleming and souganidis indiana univ math j 38 1989 pp 293 314 by considering cost functionals defined by controlled bsdes and by allowing the admissible control processes to depend on events occurring before the beginning of the game this extension of the class of admissible control processes has the consequence that the cost functionals become random variables however by making use of a girsanov transformation argument which is new in this context we prove that the upper and the lower value functions of the game remain deterministic apart from the fact that this extension of the class of admissible control processes is quite natural and reflects the behavior of the players who always use the maximum of available information its combination with bsde methods in particular that of the notion of stochastic backward semigroups introduced by peng bsde and stochastic optimizations in topics in stochastic analysis science press beijing 1997 allows us then to prove a dynamic programming principle for both the upper and the lower value functions of the game in a straightforward way the upper and the lower value functions are then shown to be the unique viscosity solutions of the upper and the lower hamilton jacobi bellman isaacs equations respectively for this peng s bsde method is extended from the framework of stochastic control theory into that of stochastic differential games

statistical einstein manifolds of exponential families with group invariant potential functions abstract this paper mainly contributes to a classification of statistical einstein manifolds namely statistical manifolds at the same time are einstein manifolds a statistical manifold is a riemannian manifold each of whose points is a probability distribution with the fisher information metric as a riemannian metric information geometry was developed to understand the intrinsic properties of statistical models which play important roles in statistical inference etc among all these models exponential families is one of the most important kinds whose geometric structures are fully determined by their potential functions to classify statistical einstein manifolds we derive partial differential equations for potential functions of exponential families special solutions of these equations are obtained through the ansatz method as well as group invariant solutions via reductions using lie point symmetries

information geometry of boltzmann machines a boltzmann machine is a network of stochastic neurons the set of all the boltzmann machines with a fixed topology forms a geometric manifold of high dimension where modifiable synaptic weights of connections play the role of a coordinate system to specify networks a learning trajectory for example is a curve in this manifold it is important to study the geometry of the neural manifold rather than the behavior of a single network in order to know the capabilities and limitations of neural networks of a fixed topology using the new theory of information geometry a natural invariant riemannian metric and a dual pair of affine connections on the boltzmann neural network manifold are established the meaning of geometrical structures is elucidated from the stochastic and the statistical point of view this leads to a natural modification of the boltzmann machine learning rule

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

imposing curvature restrictions on flexible functional forms abstract a general computational method for estimating the parameters of a flexible functional form subject to convexity quasi convexity concavity or quasi concavity at a point at several points or over a region is set forth and illustrated with an example

short cuts to dynamic factor demand modelling abstract by means of so called virtual or shadow prices short run factor demands short run marginal costs etc can be derived from any long run cost function the traditional approach short run restricted conditional variable cost functions is criticized and it is also shown that technological change scale effects etc can be added to any cost function by means of disembodied factor augmenting efficiency indexes easing the interpretations of the effects but without loss of flexibility it is shown that the trend and scale parameters of the long run translog cost function can be directly translated into trend and scale parameters of such efficiency indexes the techniques are illustrated on the well known berndt wood data set using a diewert long run generalized leontief gl cost function and assuming that capital and labour are quasi fixed

risk sensitive control with hara utility a control methodology based on the hyperbolic absolute risk averse hara utility function is presented as an alternative to the exponential of an integral approach to finding robust controllers the work is inspired by the intuition that hara controllers while being robust may give better performance than exponential controllers in normal situations the hara problem is shown to be equivalent to a certain differential game and the asymptotic properties of the hara problem and this differential game are studied as an example a linear quadratic hara problem is studied where the problem of finding a robust hara controller is proved to be equivalent to solving a standard linear quadratic problem for a system with a higher noise intensity this reveals an interesting relationship between robustness and uncertainty

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

an optimal control problem for mean field forward backward stochastic differential equation with noisy observation abstract this article is concerned with an optimal control problem derived by mean field forward backward stochastic differential equation with noisy observation where the drift coefficients of the state equation and the observation equation are linear with respect to the state and its expectation the control problem is different from the existing literature concerning optimal control for mean field stochastic systems and has more applications in mathematical finance e g asset liability management problem with recursive utility systematic risk model using a backward separation method with a decomposition technique two optimality conditions along with two coupled forward backward optimal filters are derived linear quadratic optimal control problems for mean field forward backward stochastic differential equations are studied

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

testing for separable functional structure using temporary equilibrium models abstract the importance that functional structure plays in the analysis of producer behavior is well known and responsible for the empirical tests of input separability hypotheses found in the contemporary literature unfortunately to our knowledge all such tests have been conducted under the maintained assumption of full factor input equilibrium in this paper we propose and implement a method for testing functional structure hypotheses when the behavioral units are permitted to be in disequilibrium the results of this more general test provide less support for the existence of input separability in two digit manufacturing than previously reported by the authors using tests assuming full equilibrium

geometrical theory of asymptotic ancillarity and conditional inference summary differential geometry is applied to the problems of defining higher order asymptotic ancillarity and of obtaining the asymptotic conditional distribution of an efficient estimator in multiparameter curved exponential families it is shown that a fundamental role is played in the asymptotic theory of estimation by a one parameter family of affine connexions and curvatures of subspaces asymptotic ancillary statistics of higher order are explicitly constructed with the help of the geometry the conditional distribution of an estimator is given in terms of the exponential curvature of the model and the mixture curvature of the ancillary subspaces associated with the estimator

linear forward backward stochastic differential equations with random coefficients solvability of linear forward backward stochastic differential equations fbsdes for short with random coefficients is studied a decoupling reduction method is introduced via which a large class of linear fbsdes with random or deterministic time varying coefficients is proved to be solvable on the other hand by means of four step scheme a riccati backward stochastic equation bsde for short for m n matrix valued processes is derived global solvability of such riccati bsdes is discussed for some special but nontrivial cases which leads to the solvability of the corresponding linear fbsdes

information geometry of turbo and low density parity check codes since the proposal of turbo codes in 1993 many studies have appeared on this simple and new type of codes which give a powerful and practical performance of error correction although experimental results strongly support the efficacy of turbo codes further theoretical analysis is necessary which is not straightforward it is pointed out that the iterative decoding algorithm of turbo codes shares essentially similar ideas with low density parity check ldpc codes with pearl s belief propagation algorithm applied to a cyclic belief diagram and with the bethe approximation in statistical physics therefore the analysis of the turbo decoding algorithm will reveal the mystery of those similar iterative methods in this paper we recapture and extend the geometrical framework initiated by richardson to the information geometrical framework of dual affine connections focusing on both of the turbo and ldpc decoding algorithms the framework helps our intuitive understanding of the algorithms and opens a new prospect of further analysis we reveal some properties of these codes in the proposed framework including the stability and error analysis based on the error analysis we finally propose a correction term for improving the approximation

relationship between backward stochastic differential equations and stochastic controls a linear quadratic approach it is well known that backward stochastic differential equations bsdes stem from the study on the pontryagin type maximum principle for optimal stochastic controls a solution of a bsde hits a given terminal value which is a random variable by virtue of an it additional martingale term and an indefinite initial state this paper attempts to explore the relationship between bsdes and stochastic controls by interpreting bsdes as some stochastic optimal control problems more specifically associated with a bsde a new stochastic control problem is introduced with the same dynamics but a definite given initial state the martingale term in the original bsde is regarded as the control and the objective is to minimize the second moment of the difference between the terminal state and the terminal value given in the bsde this problem is solved in a closed form by the stochastic linear quadratic lq theory developed recently the general result is then applied to the black scholes model where an optimal mean variance hedging portfolio is obtained explicitly in terms of the option price finally a modified model is investigated where the difference between the state and the expectation of the given terminal value at any time is taken into account

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

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

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

a new risk sensitive maximum principle in this paper a new maximum principle for the risk sensitive control problem is established one important feature of this result is that it applies to systems in which the diffusion term may depend on the control such control dependence gives rise to interesting phenomena not observed in the usual setting where control independence of the diffusion term is assumed in particular there is an additional second order adjoint equation and additional terms in the maximum condition that involve this second order process as well as the risk sensitive parameter moreover contrary to a conventional maximum principle the first order adjoint equation involved in our maximum principle is a nonlinear equation an advantage of considering this new type of adjoint equation is that the risk sensitive maximum principle derived is similar in form to its risk neutral counterpart the approach is based on the logarithmic transformation and the relationship between the adjoint variables and the value function as an example a linear quadratic risk sensitive problem is solved using the maximum principle derived

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

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

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

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

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

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

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

ex post tests for short and long run optimization abstract the purpose of this paper is to develop tests of long run equilibrium models where the long run is defined as the state where the observed levels of output and capital are consistent with optimizing behavior we use the implied relationship between a restricted translog cost function and derived demand equations to provide a series of nested tests which can be interpreted as ex post tests for short and long run optimization behavior a set of parameter restrictions on the translog system are specified for testing whether observable levels of capital and or output of a firm correspond to the long run optimal level our tests of the validity of long run equilibrium specifications are based on data for 28 german industries for the period 1960 1981 for most of the industries the set of restrictions implied by long run equilibrium had to be rejected

a new kind of accurate numerical method for backward stochastic differential equations in this paper we propose a new kind of numerical simulation method for backward stochastic differential equations bsdes we discretize the continuous bsdes on time space discrete grids use the monte carlo method to approximate mathematical expectations and use space interpolations to compute values at non grid points to demonstrate the accuracy and the effectiveness of our method several numerical examples are given

linear exponential quadratic control for mean field stochastic systems in this technical note we consider linear exponential quadratic leq control for mean field stochastic differential equations mfsdes the mfsde includes the expectation value of state and control and the objective functional is exponential of a quadratic functional in state control and their expectations we obtain the explicit optimal solution as well as the optimal cost the corresponding optimal solution is linear in state and its expectation which is characterized by the riccati differential equations rdes the results are obtained by showing that after applying the completion of squares method the remaining exponentiated stochastic integral and additional rde terms can be eliminated together by taking expectation since they constitute the associated radon nikodym derivative as an extension of the problem the leq zero sum differential game is considered for which we obtain the explicit optimal solution saddle point equilibrium as well as the optimal cost