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In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamics of their aggregated inventory considering a proper scaling limit. The resulting price impact profile is shown to depend on the characteristics and relative importance of their inventories. The model is flexible enough to reproduce the empirically documented power law behavior of the price impact function. For any choice of the market makers characteristics, optimal execution within this modeling approach can be recast as a linear-quadratic stochastic control problem. The value function and the associated optimal trading rate can be obtained semi-explicitly subject to solving a differential matrix Riccati equation. Numerical simulations are conducted to illustrate the performance of the resulting optimal liquidation strategy in relation to standard benchmarks. Remarkably, they show that the increase in performance is determined by a substantial reduction of higher order moment risk. [ABSTRACT FROM AUTHOR]

This paper considers an optimal control problem for a time-invariant linear stochastic system with discrete time, scalar unbounded control, additive noise, and a probabilistic criterion for retaining its trajectories in a given neighborhood of zero. We use dynamic programming and two-sided Bellman function estimates to derive analytical expressions for the optimal control at two time steps and a suboptimal control on any control horizon. The effectiveness of these controls is illustrated on a numerical example. [ABSTRACT FROM AUTHOR]

Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton–Jacobi–Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the only tools to provide accurate approximations. The aims of this paper is to introduce a novel fitted finite volume method to solve high dimensional degenerated HJB equation from stochastic optimal control problems in high dimension ( n ≥ 3 ). The challenge here is due to the nature of our HJB equation which is a degenerated second-order partial differential equation coupled with an optimization problem. For such problems, standard scheme such as finite difference method losses its monotonicity and therefore the convergence toward the viscosity solution may not be guarantee. We discretize the HJB equation using the fitted finite volume method, well known to tackle degenerated PDEs, while the time discretisation is performed using the Implicit Euler scheme.. We show that matrices resulting from spatial discretization and temporal discretization are M-matrices. Numerical results in finance demonstrating the accuracy of the proposed numerical method comparing to the standard finite difference method are provided. [ABSTRACT FROM AUTHOR]

This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance criterion based on the lower mean square error between the investor's wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton–Jacobi–Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper. [ABSTRACT FROM AUTHOR]

In this paper we study optimal trading strategies in a financial market in which stock returns depend on a hidden Gaussian mean reverting drift process. Investors obtain information on that drift by observing stock returns. Moreover, expert opinions in the form of signals about the current state of the drift arriving at fixed and known dates are included in the analysis. Drift estimates are based on Kalman filter techniques. They are used to transform a power utility maximization problem under partial information into an optimization problem under full information where the state variable is the filter of the drift. The dynamic programming equation for this problem is studied and closed-form solutions for the value function and the optimal trading strategy of an investor are derived. They allow to quantify the monetary value of information delivered by the expert opinions. We illustrate our theoretical findings by results of extensive numerical experiments. [ABSTRACT FROM AUTHOR]

Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in spatio-temporal systems described by partial differential equations (PDEs) among the robotics and control communities. These systems often exhibit dramatic under-actuation, high dimensionality, bifurcations, and multimodal instabilities. Their control represents many of the current-day challenges facing the robotics and automation communities. Not only are these systems challenging to control, but the design of their actuation is an NP-hard problem on its own. Recent methods either discretize the space before optimization, or apply tools from linear systems theory under restrictive linearity assumptions in order to arrive at a control solution. This manuscript provides a novel sampling-based stochastic optimization framework based entirely in Hilbert spaces suitable for the general class of semi-linear SPDEs which describes many systems in robotics and applied physics. This framework is utilized for simultaneous policy optimization and actuator co-design optimization. The resulting algorithm is based on variational optimization, and performs joint episodic optimization of the feedback control law and the actuation design over episodes. We study first and second order systems, and in doing so, extend several results to the case of second order SPDEs. Finally, we demonstrate the efficacy of the proposed approach with several simulated experiments on a variety of SPDEs in robotics and applied physics including an infinite degree-of-freedom soft robotic manipulator. [ABSTRACT FROM AUTHOR]

This article contributes to research dealing with the optimal dividend policy problem of a firm whose goal is to maximize the expected total discounted dividend payments before bankruptcy. We consider a model of a firm whose cash surplus exhibits regime switching, but unlike the existing literature, we exclude diffusion from our model. We assume that firm's cash surplus follows the telegraph process, which leads to a problem of singular stochastic control. Surprisingly, this problem turns out to be more complicated than the ones arising in the models involving diffusion. We solve this problem by using the method of variational inequalities and show that the optimal dividend policy can be of three significantly different types depending on the parameters of the model. [ABSTRACT FROM AUTHOR]

This paper considers an optimal control problem for a discrete-time stochastic system with the probability of first reaching the boundaries of a given domain as the optimality criterion. Dynamic programming-based sufficient conditions of optimality are formulated and proved. The isobells of levels 1 and 0 of the Bellman function are used for obtaining two-sided estimates of the right-hand side of the dynamic programming equation, two-sided estimates of the Bellman function, and two-sided estimates of the optimal-value function of the probabilistic criterion. A suboptimal control design method is proposed. The conditions of equivalence to an optimal control problem with a probabilistic terminal criterion are established. An illustrative example is given. [ABSTRACT FROM AUTHOR]

This paper examines an optimal control problem with a probabilistic criterion for retaining the trajectories of a discrete-time stochastic system in given sets. The dynamic programming method is employed for obtaining the isobells of levels 1 and 0 of the Bellman function, two-sided estimates for the right-hand side of the dynamic programming equation, two-sided estimates for the Bellman function, and the optimal-value function of the probabilistic criterion. These results are then used for deriving an approximate formula for the optimal control. As an illustrative example the problem of keeping an inverted pendulum in the neighborhood of an unstable equilibrium is considered. [ABSTRACT FROM AUTHOR]

In this paper, we describe the new OPTCON3 algorithm, which serves to determine approximately optimal policies for stochastic control problems with a quadratic objective function and nonlinear dynamic models. It includes active learning and the dual effect of optimizing policies, whereby optimal policies are used to learn about the stochastics of the dynamic system in addition to their immediate effect on the performance of the system. The OPTCON3 algorithm approximates the nonlinear model with a time-varying linear model and applies a procedure similar to that of Kendrick to the series of linearized models to calculate approximately optimal policies. The results for two simple economic models serve to test the OPTCON3 algorithm and compare it to previous solutions of the stochastic control problem. Initial evaluations show that the OPTCON3 approach may be promising to enhance our understanding of the adaptive economic policy problem under uncertainty. [ABSTRACT FROM AUTHOR]

We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary reserves of the banks as functions of time. The banking system model considered generalizes previous models studied in Fouque and Sun (in: Fouque and Langsam (eds) Handbook of systemic risk, Cambridge University Press, Cambridge, pp 444–452, 2013), Carmona et al. (Commun Math Sci 13(4):911–933, 2015), Garnier et al. (SIAM J Financ Math 4:151–184, 2013) and describes an homogeneous population of banks. Two distinct mechanisms are used to model the cooperation among banks and the cooperation between banks and monetary authority. These mechanisms are regulated respectively by the parameters α and γ . A bank fails when its log-monetary reserves go below an assigned default level. We call systemic risk or systemic event in a bounded time interval the fact that in that time interval at least a given fraction of the banks fails. The probability of systemic risk in a bounded time interval is evaluated using statistical simulation. A method to govern the probability of systemic risk in a bounded time interval is presented. The goal of the governance is to keep the probability of systemic risk in a bounded time interval between two given thresholds. The governance is based on the choice of the log-monetary reserves of a kind of "ideal bank" as a function of time and on the solution of an optimal control problem for the mean field approximation of the banking system model. The solution of the optimal control problem determines the parameters α and γ as functions of time, that is defines the rules of the borrowing and lending activity among banks and between banks and monetary authority. Some numerical examples are discussed. In particular during a two year period we consider the governance of systemic risk in the next year when governance decisions are taken quarterly. The systemic risk governance is tested in absence and in presence of positive and negative shocks acting on the banking system. [ABSTRACT FROM AUTHOR]

In this paper we consider a discrete-time formulation of dynamic transaction cost problems. We examine applicability of numerical discrete probability approximation as an alternative simplistic approach to solve dynamic transaction cost problems. We provide a computational study of a lattice-based heuristic method on simple transaction cost models and highlight its many advantages. The solution of these problems provides a dynamic investor with important insights as to how the portfolio should be re-balanced when faced with transaction costs. [ABSTRACT FROM AUTHOR]

In this paper, the optimal control problem for a discrete-time stochastic system with a general-form probabilistic criterion is considered. Using dynamic programming and the properties of the Bellman function, new two-sided bounds of this function that refine the earlier results are constructed. The derived bounds are then adopted to justify the application of the modified strategy that is optimal in the two-step investment portfolio management problem under risk to the corresponding multistep problem. An example that illustrates the advantages of such a strategy over other well-known strategies is given. [ABSTRACT FROM AUTHOR]

This paper studies a safe intercept navigation which accounts for the uncertainty of other vehicles' trajectories, avoids collisions and any other positions in which vehicle safety is compromised. Since the number of vehicles can vary with time, it is important that the navigation strategy can quickly adjust to the current number of vehicles, i.e, that it scales well with the number of vehicles. The scalable strategy is based on a stochastic optimal control problem formulation of safe navigation in the presence of a single vehicle, denoted as the one-on-one vehicle problem. It is shown that safe navigation in the presence of multiple vehicles can be solved exactly as an auxiliary Markov decision problem. This allows us to approximate the solution based on the one-on-one vehicle optimal control solution and achieve scalable navigation. Our work is illustrated by a numerical example of safely navigating a vehicle in the presence of four other vehicles and by a robot experiment. [ABSTRACT FROM AUTHOR]

By means of stochastic optimal control, this paper aims at studying the shadow pricing of renewable natural resources in uncertainty. Two cases are considered, respectively centralized and decentralized control processes. The decentralized control is in the form of a stochastic control of the state vector distributed among several agents. In both cases, the optimal control path minimizing the cost function, which is a decreasing function of time, corresponds to the real option valuation. The latter is a cost-effective optional investment in the resource stock preservation in uncertainty. The results obtained from numerical simulations show coherence with those encountered in the literature on option pricing. [ABSTRACT FROM AUTHOR]

Consideration was given to the design of the optimal control of the general discrete stochastic system with a criterion as the probability of the state vector sojourn in the given sets at each time instant. Derived were relations of the dynamic programming enabling one to establish an optimal solution in the class of Markov strategies without extension of the state vector with subsequent reduction to an equivalent problem with the probabilistic terminal criterion. Consideration was given to the problem of one-parameter correction of the flying vehicle trajectory. An analytical solution was established. [ABSTRACT FROM AUTHOR]

This paper analyzes an augmented political business cycle model taking into account the effect of employment creation decisions by the ruling party jointly on inflation and growth. The objective is to maximize voter support in the next election that depends on the rate of unemployment as well as that of growth and inflation. We allow for stochasticity in the New Keynesian Phillips Curve model for the relationship between inflation and unemployment as well as in a benchmark labour productivity function for analyzing the growth rate. We provide explicit solution paths of the affine Markov control problem that results from our formulation. We also provide numerical illustrations with plausible parametric configurations to generate more insight into our model. Our results are broadly in line with the conventional wisdom of Phillips curve, with inflation and unemployment being roughly negatively related. The growth rate is, as expected, negatively related to the unemployment. We observe that, in the sequel, it is the lowering of the rate of inflation that provides support for the ruling party. Thus, electoral pressures drive the government to engage in cost control rather than productive investment (e.g., boosting employment or output growth). [ABSTRACT FROM AUTHOR]

We consider the optimal control problem for quasilinear stochastic systems with continuous time whose coefficients have a generally non-linear dependence on the program control. We establish sufficient conditions for a strong and weak relative minimum. We give examples of using the resulting conditions for constructing optimal control in a nonlinear onedimensional problem and in a two-dimensional linear problem with information constraints and analyze the possible results. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of optimal management of renewable resources such as agricultural commodities and fishery production. For that purpose, we consider the population associated with such commodities and assume that its size evolves according to a logistic growth model with a predation term given by a Holling type- n functional response. Additionally, we assume that such population is subject to random fluctuations, modeled by a diffusive term driven by a one-dimensional Brownian motion and having a power-type coefficient, thus endowing the model under consideration with the property of having constant elasticity of variance. Since the stochastic differential equation associated with this model does not fit the standard assumptions in the stochastic optimal control literature, namely sublinear growth, we develop an appropriate version of the dynamic programming principle for the problem under consideration herein, proceeding also to provide a characterization of the optimal harvesting strategies and discuss some qualitative properties of the corresponding value function. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge-Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications. [ABSTRACT FROM AUTHOR]

Recently, the optimization-by-inference approach has been proposed as a new means for solving high-dimensional optimization problems quickly. Approximate Inference COntrol (AICO) is one of the most successful and promising methods that implement the optimization-by-inference approach. AICO is able to solve stochastic optimal control problems and has already been successfully used in many applications. However, it is known that the iterative inference of AICO sometimes fails to converge to the optimal solution. To make the optimization more robust, in this paper, we propose to take model uncertainty into account. In AICO, the cost function to be minimized is accurate around a particular state of a given stochastic system, but the accuracy is uncertain in regions far from that state. Because using such an uncertain function is harmful to the convergence, we modify AICO, so that it does not use the function in uncertain regions. Our method is easy to implement and does not add much computational time to the original AICO. Experiments using two different scenarios show that our method substantially improves AICO in terms of the rate at which the algorithm produces convergent results. [ABSTRACT FROM AUTHOR]

A modification was proposed for the relations of the method of dynamic programming in the problems of optimal stochastic control of the discrete systems by the probabilistic performance criterion. It enabled one to simplify the process of finding the optimal Markov strategy and obtain a suboptimal solution. Its efficiency was verified by the examples of maneuver optimization of the stationary satellite in the neighborhood of a geostationary orbit. An explicit form of the optimal control for the bilinear system with probabilistic terminal criterion was determined using the results obtained. [ABSTRACT FROM AUTHOR]

This paper deals with an offset control of traffic signals using a cellular automaton traffic model. A stochastic optimal control method for distributed traffic signals is modified to achieve coordinated traffic signal control with the proposed offset control method. In the proposed coordinated traffic signal control method, splits of each cycle and common cycle length are calculated using a modified stochastic optimal control method, and then the offset is calculated using an estimation method based on a modified CA traffic model at intervals. Also, simulations are carried out at multiple intersections using a micro traffic simulator. The effectiveness of the proposed coordinated control method is proved by comparing with other traffic signal control methods such as pre-timed signal control, two types of the traditional coordinated control and distributed control. [ABSTRACT FROM AUTHOR]

This paper is devoted to the optimal control problem of switching system in which constraints on the state variable are given by inclusions. Using Ekeland's variational principle, second-order necessary condition of optimality for stochastic switching systems with constraints is obtained, and transversality conditions for switching law are established. [ABSTRACT FROM AUTHOR]

This paper deals with the coordination of production, replenishment and inspection decisions for a manufacturing-oriented supply chain with a failure-prone transformation stage, random lead time and imperfect delivered lots. Upon reception of the lot, the manufacturer executes an acceptance sampling plan with a zero non-conforming criterion. If the sample does not contain non-conforming items, the lot is accepted; otherwise, it is rejected. In this work, two strategies regarding the refused sampled lot are studied. The first one involves a return of the lot to the supplier, who commits to improving the quality of the lot, while the second assumes that the manufacturer performs a 100 % inspection and rectification operation. This work presents two main objectives. The first one is to jointly optimize, in a stochastic and dynamic context, the ordering point of raw material, the lot size of raw material, the final product inventory threshold and the severity of the sampling plan using a simulation-based optimization approach. The second one is to determine the best of the two quality control strategies. The in-depth study has shown that no strategy could be preferred in all the cases. For this reasons, we present an easy decision-making tool (indifference curves) to help the manager select the best quality control strategy when considering the entire supply chain. [ABSTRACT FROM AUTHOR]

This paper presents an existence and uniqueness result for a kind of forward-backward stochastic differential equations (FBSDEs for short) driven by Brownian motion and Poisson process under some monotonicity conditions. By virtue of the conclusion of FBSDEs, we solve a linear-quadratic stochastic optimal control problem for forward-backward stochastic systems with random jumps. Moreover, we also solve a linear-quadratic nonzero-sum stochastic differential game problem. We obtain explicit forms of the unique optimal control and the unique Nash equilibrium point, respectively. [ABSTRACT FROM AUTHOR]

In this paper, a real time stochastic optimal control method for traffic signals of asymmetrical intersection is proposed. A modified cellular automaton (CA) traffic model and Bayesian network (BN) model are used to predict the traffic jams. Here, the calculation for priori probabilistic of outflows at different traffic signals is modified based on the actual situation. In addition, PSO algorithm is used to search optimal traffic signals based on the stochastic model. Finally, the effectiveness of the proposed method is shown through simulations at an asymmetrical intersection using a micro-traffic simulator. [ABSTRACT FROM AUTHOR]

In this paper, a real-time stochastic optimal control method of traffic signal is modified. In addition, H-GA-PSO algorithm is proposed to search optimal traffic signals based on the stochastic model. The H-GA-PSO algorithm is a modified Hierarchical Particle Swarm Optimization (H-PSO) algorithm based on Genetic Algorithm (GA) processing. Finally, the effectiveness of the stochastic optimal control method with H-GA-PSO algorithm is shown through simulations at multiple intersections using a micro-traffic simulator. [ABSTRACT FROM AUTHOR]

An efficient usage of available resources is a substantial requirement for the successful design of networked control systems. Recent results indicate major benefits of event-based control compared to conventional designs, when resources such as communication, energy, and computation, are sparse. This paper considers multiple entities of heterogeneous control systems whose feedback loops are coupled through a common communication medium. The design of the decentralized event-triggering control system is formulated as an average-cost problem that aims at the minimization of a social cost criterion. A state aggregation technique is used to develop a bi-level design method, which divides into a local average-cost problem within every subsystem and a global resource allocation problem assigning optimal transmission rates to every subsystem. Stability conditions are derived that guarantee stochastic stability of the aggregate system. Under these conditions, it is shown that the design approach is asymptotically optimal as the number of subsystems increases. [ABSTRACT FROM AUTHOR]

For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step t, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time steps t, t,..., T; at the next time step t, he is able to formulate a new optimization problem starting at time t that yields a new sequence of optimal decision rules. This process can be continued until the final time T is reached. A family of optimization problems formulated in this way is said to be dynamically consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of dynamic consistency, well-known in the field of economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (Ann. Oper. Res. 152(1):5-22, ) and studied in the stochastic programming framework by Shapiro (Oper. Res. Lett. 37(3):143-147, ) and for Markov Decision Processes (MDP) by Ruszczynski (Math. Program. 125(2):235-261, ). We here link this notion with the concept of 'state variable' in MDP, and show that a significant class of dynamic optimization problems are dynamically consistent, provided that an adequate state variable is chosen. [ABSTRACT FROM AUTHOR]

This paper deals with a theoretical stochastic dynamic optimization model for the external financing of firms. We aim at searching for the best intensity of payment that a financier has to apply to a company in order to have a loan repaid. The techniques involved are related to the optimal control theory with exit time. We follow a dynamic programming approach. Our model also presents a distinction between the legal and the illegal financier, and a theoretical comparison analysis of the results is presented. Some numerical examples provide further validation of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we study the situation, where the opportunity is given to invest into a government-owned business by partial privatization to a private company. After payment of an initial installment cost, the private company's investments are flexible within a range [0, k] until the business is completed. We model the problem in a real option framework, using geometric mean reversion to describe the dynamics of the business. We determine the optimal time for the private company to enter and pay the initial installment cost as well as the optimal dynamic investment strategy that it follows afterward. For the latter, analytic solution cannot be obtained. We use quadratic splines in order to solve the corresponding dynamic programming problem. Finally, we determine the optimal degree of privatization in our model from the government's perspective. [ABSTRACT FROM AUTHOR]

We studied the feedback maximization of reliability of multi-degree-of-freedom (MDOF) quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Itô equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example. [ABSTRACT FROM AUTHOR]

A category of Distributed Real-Time Systems (DRTS) that has multiprocessor pipeline architecture is increasingly used. The key challenge of such systems is to guarantee the end-to-end deadlines of aperiodic tasks. This paper proposes an end-to-end deadline control model, called Linear Quadratic Stochastic Optimal Control Model (LQ-SOCM), which features a distributed feedback control that dynamically enforces the desired performance. The control system considers the aperiodic task arrivals and execution times’ variation as the two external factors of the system unpredictability. LQ-SOCM uses discrete time state space equation to describe the real-time computing system. Then, in the actuator design, a continuous manner is adopted to deal with discrete QoS (Quality of Service) adaptation. Finally, experiments demonstrate that the system is globally stable and can statistically provide the end-to-end deadline guarantee for aperiodic tasks. At the same time, LQ-SOCM is capable of effectively improving the system throughput. [ABSTRACT FROM AUTHOR]

This paper considers a partial differential equation (PDE) approach to evaluate coherent risk measures for derivative instruments when the dynamics of the risky underlying asset are governed by a Markov-modulated geometric Brownian motion (GBM); that is, the appreciation rate and the volatility of the underlying risky asset switch over time according to the state of a continuous-time hidden Markov chain model which describes the state of an economy. The PDE approach provides market practitioners with a flexible and effective way to evaluate risk measures in the Markov-modulated Black–Scholes model. We shall derive the PDEs satisfied by the risk measures for European-style options, barrier options and American-style options. [ABSTRACT FROM AUTHOR]

The constant elasticity of variance(CEV) model was constructed to study a defined contribution pension plan where benefits were paid by annuity. It also presents the process that the Legendre transform and dual theory can be applied to find an optimal investment policy during a participant’s whole life in the pension plan. Finally, two explicit solutions to exponential utility function in the two different periods (before and after retirement) are revealed. Hence, the optimal investment strategies in the two periods are obtained. [ABSTRACT FROM AUTHOR]

A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fok-ker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the implementation of a new method to control the production rate of manufacturing systems, based on the combination of stochastic optimal control theory, discrete event simulation, experimental design and response surface methodology is outlined. The system under study consists of several parallel machines, multiple-product manufacturing system. Machines are subject to failures and repairs and their capacity process is assumed to be a finite state Markov chain throughout the analytical control model. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. The structure of the hedging point policy is then parameterized by factors representing the thresholds of involved products. With such a policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal control policy. We obtain that the hedging point policy is also applicable to a wide variety of complex problems including non-exponential failure and repair times distributions and random demand rates. Analytical solutions may not be easily obtained for such complex situations. [ABSTRACT FROM AUTHOR]

Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio's semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation. [ABSTRACT FROM AUTHOR]

The subject of this paper is modelling and optimal control of consumption and exploration of non-renewable resources via piecewise-deterministic Markov processes (PDP). In general, one assumes that new reserves are found at random times T1, T2, T3,…, where the inter-arrival times are exponentially distributed. The amount of resource found at each Ti is also a random variable with a given distribution. This process falls into the category of PDP. In this paper, we clearly show bow one can apply the PDP optimal control theory to the optimal consumption and exploration of non-renewable resources under uncertain exploration. The advantage of using a PDP model is that no matter how complicated the dynamics, utility function and distribution functions are, as long as they satisfy some mild assumptions, one can easily transform the problem into a deterministic optimal control problem, which can be solved iteratively with guaranteed convergence for the value function. [ABSTRACT FROM AUTHOR]