on singular control problems with state constraints and regime switching this paper investigates a singular stochastic control problem for a multi dimensional regime switching diffusion process confined in an unbounded domain the objective is to maximize the total expected discounted rewards from exerting the singular control such a formulation stems from application areas such as optimal harvesting multiple species and optimal dividends payments schemes in random environments with the aid of weak dynamic programming principle and an exponential transformation we characterize the value function to be the unique constrained viscosity solution of a certain system of coupled nonlinear quasi variational inequalities several examples are analyzed in detail to demonstrate the main results

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

optimal ordering policy for inventory systems with quantity dependent setup costs we consider a continuous review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a brownian motion with a positive drift assuming the holding and shortage cost to be a convex function of the inventory level we obtain the optimal ordering policy that minimizes the long run average cost by a lower bound approach to tackle some technical issues in the lower bound approach under the quantity dependent setup cost assumption we establish a comparison theorem that enables one to prove the global optimality of a policy by examining a tractable subset of admissible policies since the smooth pasting technique does not apply to our brownian inventory model we also propose a selection procedure for computing optimal policy parameters when the setup cost is a step function

optimal impulse control for a multidimensional cash management system with generalized cost functions abstract we consider the optimal control of a multidimensional cash management system where the cash balances fluctuate as a homogeneous diffusion process in r n we formulate the model as an impulse control problem on an unbounded domain with unbounded cost functions under general assumptions we characterize the value function as a weak solution of a quasi variational inequality in a weighted sobolev space and we show the existence of an optimal policy moreover we prove the local uniform convergence of a finite element scheme to compute numerically the value function and the optimal cost we compute the solution of the model in two dimensions with linear and distance cost functions showing what are the shapes of the optimal policies in these two simple cases finally our third numerical experiment computes the solution in the realistic case of the cash concentration of two bank accounts made by a centralized treasury

pointwise error estimates for a class of elliptic quasi variational inequalities with nonlinear source terms in this paper we derive l error estimates of a piecewise linear approximation method for a class of elliptic quasi variational inequalities qvis with nonlinear source terms our approach stands on a discrete l stability property with respect to the right hand side in linear elliptic qvis

a solvable one dimensional model of a diffusion inventory system we analyse the optimal ordering policy for impulse control of a one product inventory system subject to a demand modelised by a diffusion process the purpose is to minimize the expected discounted cost that includes a fixed set up cost and linear costs of purchase storage and shortage the optimal cost is explicitly obtained as the smoothest solution of a quasi variational inequality derived from the optimal principle of dynamic programming the optimal s s policy is determined as the unique solution of a system of algebraic equations

condition numbers of hankel matrices for exponential weights abstract we obtain the rate of growth of the largest eigenvalues and euclidean condition numbers of the hankel matrices i t j k w 2 t d t j k 0 n for a general class of even exponential weights w 2 exp 2 q on an interval i as particular examples we discuss q x x on i r and q x d 2 x 2 on i d d

the condition number of real vandermonde krylov and positive definite hankel matrices we show that the euclidean condition number of any positive definite hankel matrix of order n geq 3 may be bounded from below by gamma n 1 16n with gamma exp 4 cdot it catalan pi approx 3 210 and that this bound may be improved at most by a factor 8 gamma n similar estimates are given for the class of real vandermonde matrices the class of row scaled real vandermonde matrices and the class of krylov matrices with hermitian argument improved bounds are derived for the case where the abscissae or eigenvalues are included in a given real interval our findings confirm that all such matrices including for instance the famous hilbert matrix are ill conditioned already for moderate order as application we describe implications of our results for the numerical condition of various tasks in numerical analysis such as polynomial and rational i nterpolation at real nodes determination of real roots of polynomials computation of coefficients of orthogonal polynomials or the iterative solution of linear systems of equations

l asymptotic behavior for a finite element approximation in parabolic quasi variational inequalities related to impulse control problem abstract in this paper the parabolic quasi variational inequalities are transformed into a noncoercive elliptic quasi variational inequalities a new iterative discrete algorithm is proposed to show the existence and uniqueness and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation the proposed approach stands on a discrete l stability property with respect to the right hand side and obstacle defined as an impulse control problem

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

the finite element approximation of variational inequalities related to ergodic control problems abstract in this paper we study the numerical approximation of variational inequalities vi where the discount factor i e the zero order term is set to 0 optimal error estimates are proved in the l norm using the concept of subsolutions

small eigenvalues of large hankel matrices in this paper we investigate the smallest eigenvalue denoted as n of a n 1 n 1 hankel or moments matrix associated with the weight w x exp x x 0 0 in the large n limit using a previous result the asymptotics for the polynomials pn z z 0 orthonormal with respect to w which are required in the determination of n are found adopting an argument of szegothe asymptotic behaviour of n for where the related moment problem is determinate is derived this generalizes the result given by szegofor 1 it is shown that for the smallest eigenvalue of the infinite hankel matrix is zero while for 0 it is greater then a positive constant this shows a phase transition in the corresponding hermitian random matrix model as the parameter varies with identified as the critical point the smallest eigenvalue at this point is conjectured

robust inventory management an optimal control approach we formulate and solve static and dynamic models of inventory management that lie at the intersection of robust optimization and optimal control theory our objective is to minimize cumulative ordering holding and shortage costs over a horizon 0 t where the variable is a nonnegative ordering rate function q t 2 0 t the demand rate function d t is unknown and is only assumed to belong to an uncertainty set d t l2 0 t a 1 t 0td t dt b a d t b t 0 t this set is motivated by the strong law of large numbers for stochastic processes limt 1 t 0td t dt where is the mean drift we analyze a static model where the ordering rate function must be fully specified at time zero and three dynamic variants where re optimizations are allowed during the planning horizon 0 t at prespecified review epochs in the dynamic models at review epoch 0 t the past demand on 0 is observable in the first dynamic model we ignore this information and define a variant of that i

instantaneous control of brownian motion a controller continuously monitors a storage system such as an inventory or bank account whose content z zt t 0 fluctuates as a 2 brownian motion in the absence of control holding costs are incurred continuously at rate h zt at any time the controller may instantaneously increase the content of the system incurring a proportional cost of r times the size of the increase or decrease the content at a cost of l times the size of the decrease we consider the case where h is convex on a finite interval and h outside this interval the objective is to minimize the expected discounted sum of holding costs and control costs over an infinite planning horizon it is shown that there exists an optimal control limit policy characterized by two parameters a and b a b roughly speaking this policy exerts the minimum amounts of control sufficient to keep zt a b for all t 0 put another way the optimal control limit policy imposes on z a lower reflecting barrier at a an

discrete minimum and maximum principles for finite element approximations of non monotone elliptic equations uniform lower and upper bounds for positive finite element approximations to semilinear elliptic equations in several space dimensions subject to mixed dirichlet neumann boundary conditions are derived the main feature is that the non linearity may be non monotone and unbounded the discrete minimum principle provides a positivity preserving approximation if the discretization parameter is small enough and if some structure conditions on the non linearity and the triangulation are assumed the discrete maximum principle also holds for degenerate diffusion coefficients the proofs are based on stampacchia s truncation technique and on a variational formulation both methods are settled on careful estimates on the truncation operator

on an investment consumption model with transaction costs this paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log normal diffusions we suppose that transactions between the assets incur a cost proportional to the size of the transaction the problem is to maximize the total utility of consumption dynamic programming leads to a variational inequality for the value function existence and uniqueness of a viscosity solution are proved the variational inequality is solved by using a numerical algorithm based on policies iterations and multigrid methods numerical results are displayed for n 1 and n 2

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

a measure approach for continuous inventory models discounted cost criterion this paper develops a new approach to the solution of impulse control problems for continuous inventory models under a discounted cost criterion the analysis imbeds this stochastic problem in two different infinite dimensional linear programs parametrized by the initial inventory level x 0 by concentrating on particular functions and capturing the expected discounted behavior of the inventory level process and ordering decisions as measures the first imbedding then naturally leads to the minimization of a nonlinear function representing the cost associated with an s s ordering policy and an optimizing pair determines optimal levels s s the lower bound arising from this imbedding is tight when x 0 geq s but is a strict lower bound when x 0 s solving the first linear program determines the value function in the no order region and is critical to the formulation of the second linear program the dual of the second linear program is then solved to provide a tight lower bound

on optimal harvesting problems in random environments this paper investigates the optimal harvesting strategy for a single species living in random environments whose population growth is given by a regime switching diffusion harvesting acts as a stochastic control on the size of the population the objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting up to the time of extinction of the species the income rate is allowed to be state and environment dependent this is a singular stochastic control problem with both the extinction time and the optimal harvesting policy depending on the initial condition one aspect of receiving payments up to the random time of extinction is that small changes in the initial population size may significantly alter the extinction time when using the same harvesting policy consequently one no longer obtains continuity of the value function using standard arguments for either regular or singular control problems having a fixed time horizon this paper introduces a new sufficient condition under which the continuity of the value function for the regime switching model is established further it is shown that the value function is a viscosity solution of a coupled system of quasi variational inequalities the paper also establishes a verification theorem and based on this theorem an varepsilon optimal harvesting strategy is constructed under certain conditions on the model two examples are analyzed in detail

smallest eigenvalue of large hankel matrices at critical point comparing conjecture with parallelised computation abstract we propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill conditioned hankel matrices it is based on the ldlt decomposition and involves finding a k k sub matrix of the inverse of the original n n hankel matrix h n 1 the computation involves extremely high precision arithmetic message passing interface and shared memory parallelisation we demonstrate that this approach achieves good scalability on a high performance computing cluster hpcc which constitutes a major improvement of the earlier approaches we use this method to study a family of hankel matrices generated by the weight w x e x supported on 0 and 0 such weight generates a hankel determinant a fundamental object in random matrix theory in the situation where 1 2 the smallest eigenvalue tends to 0 exponentially fast if 1 2 it is conjectured that the smallest eigenvalue tends to 0 algebraically with a precise exponent the algorithm run on the hpcc producing a fantastic match between the theoretical value of 2 and the numerical result

l error estimate for a system of elliptic quasi variational inequalities with noncoercive operators this paper deals with the standard finite element approximation of a noncoercive system of quasi variational inequalities qvis arising in stochastic control problems we improve a result obtained in boulbrachene comput math appl 45 983 989 2003 and establish the optimal l convergence order making use of the concepts of subsolutions and discrete regularity

on finite element approximation in the l norm of variational inequalities we are interested in the approximation in thel norm of variational inequalities with non linear operators and somewhat irregular obstacles we show that the order of convergence will be the same as that of the equation associated with the non linear operator if the discrete maximum principle is verified

optimal switching with constraints and utility maximization of an indivisible market this work focuses on optimal switching with constraints our motivation stems from utility maximization of an indivisible market the dynamic programming approach is used the value function is characterized as the unique viscosity solution of a quasi variational inequality the unbounded domain introduces new challenges by studying the sample paths of the diffusion at the boundary a sufficient condition for the continuity of the value function is provided yielding the desired characterization not only are the results of this work applicable to the utility maximization problem but also they can be used for general optimal switching problems with finite regimes

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

error estimates for approximate solutions to bellman equations associated with controlled jump diffusions we derive error estimates for approximate viscosity solutions of bellman equations associated to controlled jump diffusion processes which are fully nonlinear integro partial differential equations two main results are obtained i error bounds for a class of monotone approximation schemes which under some assumptions includes finite difference schemes and ii bounds on the error induced when the original levy measure is replaced by a finite measure with compact support an approximation process that is commonly used when designing numerical schemes for integro partial differential equations our proofs use and extend techniques introduced by krylov and barles jakobsen

impulse control of brownian motion consider a storage system such as an inventory or cash fund whose content fluctuates as a 2 brownian motion in the absence of control holding costs are continuously incurred at a rate proportional to the storage level and we may cause the storage level to jump by any desired amount at any time except that the content must be kept nonnegative both positive and negative jumps entail fixed plus proportional costs and our objective is to minimize expected discounted costs over an infinite planning horizon a control band policy is one that enforces an upward jump to q whenever level zero is hit and enforces a downward jump to q whenever level s is hit 0 q q s we prove the existence of an optimal control band policy and calculate explicitly the optimal values of the critical numbers q q s

a fuzzy stochastic single period model for cash management the major purpose of this paper is to apply a stochastic single period inventory management approach to analyze optimal cash management policies with fuzzy cash demand based on fuzzy integral method so that total cost is minimized we will find that after defuzzification the cash raising amounts and the total costs between the fuzzy case and the crisp case are slightly different when the variation of cash demand is small as a result we point out that the fuzzy stochastic single period model is one extension of the crisp models in any case one may conclude that a conscientious analysis in fuzzy mathematics like that presented in this paper provides a financial decision maker with a deeper insight into the more real cash management problem

optimal mixed impulse equity insurance control problem with reinsurance we investigate an optimal financing and dividend control problem of an insurance company facing fixed and proportional transaction costs the goal of the company is to maximize the expected present value of future dividends after deduction of the equity issuance until the time of bankruptcy we formulate the problem as a mixed classical impulse control and discuss the problem using the hjb dynamic programming approach a viscosity solution is considered and its uniqueness is established we also give results for the regularity and structure of the value function and the optimal policy of the control problem

optimal policies for brownian inventory systems with a piecewise linear ordering cost we consider a stochastic inventory system with general piecewise linear ordering cost the cumulative demand is modeled as a brownian motion process the ordering cost function is neither convex nor concave it may not be monotone and it is not even necessarily continuous and it includes most ordering cost functions studied in the literature e g economies of scale or dis economies of scale all unit discount or incremental discount and multiple setup costs as special cases in addition to ordering cost the system incurs the usual holding shortage cost and the objective is to minimize the average system cost per unit of time despite the complexity in the ordering cost function we show that an optimal control policy is very simple it is either an s s policy or a one sided singular control policy

transverse vibrations of simply supported rectangular plates with two rectangular cutouts an approximate solution is proposed in the present paper whereby the displacement amplitude is expressed in terms of a double fourier series which satisfies identically the boundary conditions and which constitutes the exact solution in the case of a solid rectangular plate of uniform thickness the rayleigh ritz method is then applied to determine the fundamental frequency coefficient

finite element error estimates in non energy norms for the two dimensional scalar signorini problem this paper is concerned with error estimates for the piecewise linear finite element approximation of the two dimensional scalar signorini problem on a convex polygonal domain varomega using a cea type lemma a supercloseness result and a non standard duality argument we prove w 1 p varomega l infty varomega w 1 infty varomega and h 1 2 partial varomega error estimates under reasonable assumptions on the regularity of the exact solution and l p varomega error estimates under comparatively mild assumptions on the involved contact sets the obtained orders of convergence turn out to be optimal for problems with essentially bounded right hand sides our results are accompanied by numerical experiments which confirm the theoretical findings

the smallest eigenvalue of large hankel matrices generated by a singularly perturbed laguerre weight an asymptotic expression of the orthonormal polynomials pn z as n associated with the singularly perturbed laguerre weight w x t x e x tx x 0 1 t 0 is derived based on this we establish the asymptotic behavior of the smallest eigenvalue n of the hankel matrix generated by the weight w x t

impulse control of brownian motion the constrained average cost case when a manufacturer places repeated orders with a supplier to meet changing production requirements he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes we consider an inventory whose content fluctuates as a brownian motion in the absence of control at any moment a controller can adjust the inventory level by any positive or negative quantity but incurs both a fixed cost and a cost proportional to the magnitude of the adjustment the inventory level must be nonnegative at all times and continuously incurs a linear holding cost the objective is to minimize long run average cost we show that control band policies are optimal for the average cost brownian control problem and explicitly calculate the parameters of the optimal control band policy this form of policy is described by three parameters q q s 0 q q s when the inventory falls to zero rises to s the controller expedites curtails shipments to return it to q q employing apparently new techniques based on methods of lagrangian relaxation we show that this type of policy is optimal even with constraints on the size of adjustments and on the maximum inventory level we also extend these results to the discounted cost problem

finite horizon optimal stopping of time discontinuous functionals with applications to impulse control with delay we study finite horizon optimal stopping problems for continuous time feller markov processes the functional depends on time state and external parameters and may exhibit discontinuities with respect to the time variable both left and right hand discontinuities are considered we investigate the dependence of the value function on the parameters on the initial state of the process and on the stopping horizon we construct varepsilon optimal stopping times and provide conditions under which an optimal stopping time exists we demonstrate how to approximate this optimal stopping time by solutions to discrete time problems our results are applied to the study of impulse control problems with finite time horizon decision lag and execution delay

inventory control for spectrally positive levy demand processes a new approach to solve the continuous time stochastic inventory problem using the fluctuation theory of levy processes is developed this approach involves the recent developments of the scale function that is capable of expressing many fluctuation identities of spectrally one sided levy processes for the case with a fixed cost and a general spectrally positive levy demand process we show the optimality of an s s policy the optimal policy and the value function are concisely expressed via the scale function numerical examples under a levy process in the family with jumps of infinite activity are provided to confirm the analytical results furthermore the case with no fixed ordering costs is studied

solving hankel matrix approximation problem using semidefinite programming positive semidefinite hankel matrices arise in many important applications some of their properties may be lost due to rounding or truncation errors incurred during evaluation the problem is to find the nearest matrix to a given matrix to retrieve these properties the problem is converted into a semidefinite programming problem as well as a problem comprising a semidefined program and second order cone problem the duality and optimality conditions are obtained and the primal dual algorithm is outlined explicit expressions for a diagonal preconditioned and crossover criteria have been presented computational results are presented a possibility for further improvement is indicated

a numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit gmwb in this paper we outline an impulse stochastic control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit gmwb assuming the policyholder is allowed to withdraw funds continuously we develop a numerical scheme for solving the hamilton jacobi bellman hjb variational inequality corresponding to the impulse control problem we prove the convergence of our scheme to the viscosity solution of the continuous withdrawal problem provided a strong comparison result holds the scheme can be easily generalized to price discrete withdrawal contracts numerical experiments are conducted which show a region where the optimal control appears to be non unique

optimization in first passage resetting we investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold in an infinite domain this process is nonstationary and its probability distribution exhibits rich features in a finite domain we define a nontrivial optimization in which a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset point we derive the condition to optimize the net gain in this system namely the reward minus the cost

approximation of obstacle problems by continuation methods nonlinear variational inequalities associated with obstacle problems are considered which may exhibit multiple solutions and turning points a predictor corrector continuation method for following a solution branch is presented essentially it is shown that regular or simple singular solutions of the nonlinear eigenvalue problem are regular for an augmented problem the main difficulty here is due to the fact that the equations are not differentiable in the frechet sense the numerical schemes that are used in the implementation of the method are developed for the predictor step a deflated block algorithm is used and for the corrector step algorithms are set up using projected sor projected newton and projected preconditioned conjugate gradients the efficiency of the various algorithms is compared by applying the continuation method to a finite element discretization of a two dimensional problem numerical results are presented

infinite order cross validated local polynomial regression many practical problems require nonparametric estimates of regression func tions and local polynomial regression has emerged as a leading approach in applied settings practitioners often adopt either the local constant or local linear variants or choose the order of the local polynomial to be slightly greater than the order of the maximum derivative esti mate required but such ad hoc determination of the polynomial order may not be optimal in general while the joint determination of the polynomial order and bandwidth presents some interesting theoretical and practical challenges in this paper we propose a data driven approach towards the joint determination of the polynomial order and bandwidth provide theoretical underpinnings and demonstrate that improvements in both nite sample e ciency and rates of convergence can thereby be obtained in the case where the true data generating process dgp is in fact a polynomial whose order does not depend on the sample size our method is capable of attaining the p n rate often associated with correctly speci ed parametric models while the estimator is shown to be uniformly consistent for a much larger class of dgps theoretical underpinnings are provided and nite sample properties are examined

impulse control of multidimensional jump diffusions in finite time horizon this paper analyzes a class of impulse control problems for multidimensional jump diffusions in the finite time horizon following the basic mathematical setup from stroock and varadhan multidimensional diffusion processes springer verlag heidelberg 2006 this paper first establishes rigorously an appropriate form of the dynamic programming principle it then shows that the value function is a viscosity solution for the associated hamilton jacobi bellman equation involving integro differential operators finally under additional assumptions that the jumps are of infinite activity but are of finite variation and that the diffusion is uniformly elliptic it proves that the value function is the unique viscosity solution and has w loc 2 1 p regularity for 1 p infty

optimal control of a brownian production inventory system with average cost criterion in this paper we study a stochastic production inventory system with finite production capacity and random demand the cumulative production and demand are modeled by a two dimensional brownian motion process there is a setup cost for switching on the production and a convex holding and shortage cost and our objective is to find the optimal production inventory control that minimizes the average cost both lost sales and backlog cases are studied for the lost sales model we show that within a large class of policies the optimal production strategy is either to produce according to an s s policy or never turn on the machine at all thus it is optimal for the firm to not enter the business whereas for the backlog model we prove that the optimal production policy is always of the s s type our approach first develops a lower bound for the average cost among a large class of nonanticipating policies and then shows that the value function of the desired policy reaches the lower bound the results offer insights on the structure of the optimal control policies as well as the interplays between system parameters

an impulse control of a geometric brownian motion with quadratic costs we examine an optimal impulse control problem of a stochastic system whose state follows a geometric brownian motion we suppose that when an agent intervenes in the system it requires costs consisting of a quadratic form of the system state besides the intervention costs running costs are continuously incurred to the system and they are also of a quadratic form our objective is to find an optimal impulse control of minimizing the expected total discounted sum of the intervention costs and running costs incurred over the infinite time horizon in order to solve this problem we formulate it as a stochastic impulse control problem which is approached via quasi variational inequalities qvi under a suitable set of sufficient conditions on the given problem parameters we prove the existence of an optimal impulse control such that whenever the system state reaches a certain level the agent intervenes in the system consequently it instantaneously reduces to another level

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

a direct solution method for stochastic impulse control problems of one dimensional diffusions we consider stochastic impulse control problems where the process is driven by one dimensional diffusions impulse control problems are widely applied to financial engineering and decision making problems including the dividend payout problem portfolio optimization with transaction costs and inventory control we shall show a new mathematical characterization of the value function in the continuation region as a linear function in a certain transformed space the merits of our approach are as follows 1 one does not have to guess optimal strategies or verify the optimality via a verification lemma 2 the method of finding the solution based on the new characterization of the value function is simple and direct and thereby 3 one can handle a broader class of reward and cost functions than the conventional methods that use quasi variational inequalities

optimal impulse control of portfolios an investor has the opportunity of holding shares in n risky assets and one nonrisky asset at every time in a fixed interval t t the risky assets are governed by a stochastic differential equation at random instants of his choice he may intervene in order to rebalance his portfolio and consume a nonnegative amount of money fixed and variable transactions costs are incurred upon intervention at time t all remaining wealth is consumed the solution to the problem of maximizing total utility of consumption is given by way of quasi variational inequalities for the value function with probability one the investor only intervenes finitely many times indication of the solution of the quasi variational inequalities in the case of one risky asset with log normal prices is given together with a description of a discretization procedure

a fixed point approximation method for some noncoercive variational problems abstract this paper deals with the finite element approximation of some variational problems namely linear elliptic boundary value problems variational inequalities and quasi variational inequalities with noncoercive operators to prove optimal l error estimates we introduce a simple and direct argument combining continuous piecewise linear finite elements with the banach fixedpoint theorem

optimal consumption and investment policies allowing consumption constraints and bankruptcy an agent can distribute his wealth between two investments one with a fixed rate of return r and the other with a random rate of return modeled as a diffusion with mean r the agent seeks to maximize total discounted utility from consumption over an infinite horizon consumption may be constrained from below various models for bankruptcy including welfare are considered the agent has a strictly concave utility function for consumption however it is shown that the utility function for wealth may have convex portions thus the agent may be risk seeking the paper gives a complete treatment of the existence and nonexistence of optimal policies new theorems for the optimal control of degenerate diffusions are given as well as explicit formulas for the value function

vibrations of simply supported rectangular plates with varying thickness and same aspect ratio cutouts fil larrondo hilda angela universidad nacional de mar del plata facultad de ingenieria argentina consejo nacional de investigaciones cientificas y tecnicas argentina

the noncoercive quasi variational inequalities related to impulse control problems abstract this paper deals with the numerical analysis of noncoercive quasi variational inequalities of impulse control problems optimally l error estimates are derived using qualitative properties of both the continuous and finite element approximation solutions and the notion of subsolutions

impulse control of multidimensional jump diffusions this paper studies regularity properties of the value function for an infinite horizon discounted cost impulse control problem where the underlying controlled process is a multidimensional jump diffusion with possibly infinite activity jumps surprisingly despite these jumps we obtain the same degree of regularity as for the diffusion case at least when the jump satisfies certain integrability conditions

hamilton jacobi bellman quasi variational inequality arising in an environmental problem and its numerical discretization abstract a hamilton jacobi bellman quasi variational inequality hjbqvi for a river environmental restoration problem with wise use of sediment is formulated and its mathematical properties are analyzed a finite difference scheme with a penalization technique is then established for solving the hjbqvi the scheme is free from any iterative solvers and is unconditionally stable and convergent in the viscosity sense under certain conditions a demonstrative application example of the hjbqvi is finally presented

smooth fit principle for impulse control of multidimensional diffusion processes value functions of impulse control problems are known to satisfy quasi variational inequalities qvis a bensoussan and j l lions impulse control and quasivariational inequalities heyden son philadelphia 1984 translation of controle impulsionnel et inequations quasi variationnelles gauthier villars paris 1982 this paper proves the smooth fit c 1 property of the value function for multidimensional controlled diffusions using a viscosity solution approach we show by examples how to exploit this regularity property to derive explicitly optimal policy and value functions

double band policy for stochastic manufacturing systems in heavy traffic we consider the control of a manufacturing system producing one product the demand for this product is random the manager can produce the product at a fixed rate r or choose to stop the production each time the production is resumed a setup cost must be paid to prevent the backlog which is not allowed the manager can buy the product from outside vendors paying a fixed order cost and a variable cost there is also a linear inventory holding cost the objective is to minimize the total expected discounted cost under heavy traffic conditions i e when the production capacity is close to the average demand this problem is approximated by an impulse control problem for brownian motion which is solved explicitly the solution is then used to derive a control policy for the original system the resulting control is characterized by three parameters 0 q0 q0 s0 and is dubbed double band policy when the inventory reaches s0 the machine is turned off and it is turned on again when inventory decreases to level q0 an amount of q0 units is purchased from the outside vendor if the inventory level drops to zero we prove that this policy is nearly optimal that is the relative difference between the cost under this policy and the optimal cost is small if traffic intensity is close to one

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

finite element approximation of the volume matching problem optimal orderh 1 andl error bounds are obtained for a continuous piecewise linear finite element approximation of the volume matching problem this problem consists of minimising v 1 2 overv h 1 subject to the inequality constraintv 0 and a number of linear equality constraints the presence of the equality constraints leads to lagrange multipliers which in turn lead to complications with the standard error analysis for variational inequalities finally we consider an algorithm for solving the resulting algebraic problem

smallest eigenvalues of hankel matrices for exponential weights abstract we obtain the rate of decay of the smallest eigenvalue of the hankel matrices i t j k w 2 t dt j k 0 n for a general class of even exponential weights w2 exp 2q on an interval i more precise asymptotics for more special weights have been obtained by many authors