Добірка наукової літератури з теми "Optimal dividend control problem"

An optimal dividend problem with investment opportunities, taking into consideration a source of strategic risk is being considered, as well as the effect of market frictions on the decision process of the financial entities. It concerns the problem of determining an optimal control of the dividend under debt constraints and investment opportunities in an economy with business cycles. It is assumed that the company is to be allowed to accept or reject investment opportunities arriving at random times with random sizes, by changing its outstanding indebtedness, which would impact its capital structure and risk profile. This work mainly focuses on the strategic risk faced by the companies; and, in particular, it focuses on the manager's problem of setting appropriate priorities to deploy the limited resources available. This component is taken into account by introducing frictions in the capital structure modification process. The problem is formulated as a bi-dimensional singular control problem under regime switching in presence of jumps. An explicit condition is obtained in order to ensure that the value function is finite. A viscosity solution approach is used to get qualitative descriptions of the solution. Moreover, a lending scheme for a system of interconnected banks with probabilistic constraints of failure is being considered. The problem arises from the fact that financial institutions cannot possibly carry enough capital to withstand counterparty failures or systemic risk. In such situations, the central bank or the government becomes effectively the risk manager of last resort or, in extreme cases, the lender of last resort. If, on the one hand, the health of the whole financial system depends on government intervention, on the other hand, guaranteeing a high probability of salvage may result in increasing the moral hazard of the banks in the financial network. A closed form solution for an optimal control problem related to interbank lending schemes has been derived, subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to real bank networks by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network. Finally, a possible computation technique for the Default Risk Charge under to regulatory risk measurement processes is being considered. We focus on the Default Risk Charge measure as an effective alternative to the Incremental Risk Charge one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets emitted by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible, because of both new regulation and the high speed - low cost technology available nowadays.

A formulation of impedance control for redundant manipulators is developed as a particular case of an optimal control problem. This formulation allows the planning and design of an impedance controller that benets from the stability and eficiency of an optimal controller. Moreover, to circumvent the high computational costs of computing an optimal controller, a sub-optimal feedback controller based on the state-dependent Ricatti equation (SDRE) approach is developed. This approach is then compared with the quadratic programming (QP) control formulation, commonly used to resolve redundancy of robotic manipulators. Numerical simulations of a redundant planar 4-DOF serial link manipulator show that the SDRE control formulation offers superior performance over the control strategy based QP, in terms of stability, performance and required control effort.<br>Uma formulação do controle de impedância para manipuladores redundantes é desenvolvida como um caso particular de um problema de controle ótimo. Essa formulação permite o planejamento e projeto de um controlador de impedância que se beneficia da estabilidade e eficiência de um controlador ótimo. Para evitar lidar com os elevados custos computacionais de se computar um controlador ótimo, um controlador em malha fechada sub-ótimo, baseado na abordagem das equações de Ricatti dependentes de estado (SDRE), é desenvolvido. Essa abordagem é comparada com a formulação de um controlador baseado em programação quadrática (QP), usualmente utilizado para resolver problemas de redundância em manipuladores robóticos. Simulações numéricas de um manipulador serial plano de quatro graus de liberdade mostram que o controlador baseado em SDRE oferece performance superior em relação a um controlador baseado em programação quadrática, em termos de estabilidade, performance e esforço de controle requerido do atuador.

The H_infinity control problem is studied for linear constant coefficient descriptor systems. Necessary and sufficient optimality conditions as well as controller formulas are derived in terms of deflating subspaces of even matrix pencils for problems of arbitrary index. A structure preserving method for computing these subspaces is introduced. In combination these results allow the derivation of a numerical algorithm with advantages over the classical methods.

We consider the analysis of the scattering problem. Assume that an incoming time harmonic wave is scattered by a surface of an impenetrable obstacle. The reflected wave is determined by the surface impedance of the obstacle. In this paper we will investigate the problem of choosing the surface impedance so that a desired scattering amplitude is achieved. We formulate this control problem within the framework of the minimization of a Tikhonov functional. In particular, questions of the existence of an optimal solution and the derivation of the optimality conditions will be addressed.<br>Master of Science

Within the dividend policy literature there is no universally accepted model to explain dividend behaviour. The theoretical dividend policy literature contains a promising dynamic mathematical model based on optimal control theory formulated by Davidson (1980), in the spirit of the Modigliani-Brumberg-Yaari types of lifecyle hypothesis, but despite being published some time ago the model has not been tested empirically, possibly due to its complexity. It is the main purpose of this research study to investigate the dividend behaviour patterns of banks listed on the NYSE within this optimal control theory framework. This work unfolds in three stages as follows: initially the impacts of the different control planning horizons in determining dividend patterns are examined. Secondly, the factors that govern the control-theoretic dividend patterns are established. Finally the factors that are associated with out-performers of the control theory framework are identified. Appropriate and relevant data from NYSE banking corporations were obtained to test the effectiveness and efficiency of the control theory framework. The application of logistic regression analysis and logistic step-wise regression established the factors that govern the control-theoretic dividend patterns. The application of multiple regression analysis and step-wise regression analysis enabled this study to determine the factors that are associated with out-performers of the control theory framework. Research findings suggest that the long planning horizon model tends to be good explanator of observed dividends, suggesting that the dividend decision is not constrained by short or medium term predicted liquid asset levels. NYSE banks with control-theoretic dividend patterns were associated with the smaller banks, which perform financially well and display a strong share price record, as indicated by the high Tobin's Q ratio, strong dividend yield, a greater return on capital invested, higher leverage, and a smaller number of employees. The NYSE banks with observed dividends that out-perform the control theory framework are associated with banks that have higher profits, as indicated by the higher return on equity, and an implied expanding customer base, as suggested by the higher revenue growth rate. Outperfoming banks also have higher dividend yields, constrained by an implied internally imposed conservative retention policy, as indicated by lower payout ratios and they tend to be smaller in size. Further research in this area is required to investigate the dividend behaviour of organisations operating on other stock markets around the world, and should help to unlock the full potential that is offered by a control theory framework.

In this thesis, we develop new computational methods for three classes of dynamic optimization problems: (i) A parameter identification problem for a general nonlinear time-delay system; (ii) an optimal control problem involving systems with both input and output delays, and subject to continuous inequality state constraints; and (iii) a max-min optimal control problem arising in gradient elution chromatography.In the first problem, we consider a parameter identification problem involving a general nonlinear time-delay system, where the unknown time delays and system parameters are to be identified. This problem is posed as a dynamic optimization problem, where its cost function is to measure the discrepancy between predicted output and observed system output. The aim is to find unknown time-delays and system parameters such that the cost function is minimized. We develop a gradient-based computational method for solving this dynamic optimization problem. We show that the gradients of the cost function with respect to these unknown parameters can be obtained via solving a set of auxiliary time-delay differential systems from t = 0 to t = T. On this basis, the parameter identification problem can be solved as a nonlinear optimization problem and existing optimization techniques can be used. Two numerical examples are solved using the proposed computational method. Simulation results show that the proposed computational method is highly effective. In particular, the convergence is very fast even when the initial guess of the parameter values is far away from the optimal values.Unlike the first problem, in the second problem, we consider a time delay identification problem, where the input function for the nonlinear time-delay system is piecewise-constant. We assume that the time-delays—one involving the state variables and the other involving the input variables—are unknown and need to be estimated using experimental data. We also formulate the problem of estimating the unknown delays as a nonlinear optimization problem in which the cost function measures the least-squares error between predicted output and measured system output. This estimation problem can be viewed as a switched system optimal control problem with time-delays. We show that the gradient of the cost function with respect to the unknown state delay can be obtained via solving a auxiliary time-delay differential system. Furthermore, the gradient of the cost function with respect to the unknown input delay can be obtained via solving an auxiliary time-delay differential system with jump conditions at the delayed control switching time points. On this basis, we develop a heuristic computational algorithm for solving this problem using gradient based optimization algorithms. Time-delays in two industrial processes are estimated using the proposed computational method. Simulation results show that the proposed computational method is highly effective.For the third problem, we consider a general optimal control problem governed by a system with input and output delays, and subject to continuous inequality constraints on the state and control. We focus on developing an effective computational method for solving this constrained time delay optimal control problem. For this, the control parameterization technique is used to approximate the time planning horizon [0, T] into N subintervals. Then, the control is approximated by a piecewise constant function with possible discontinuities at the pre-assigned partition points, which are also called the switching time points. The heights of the piecewise constant function are decision variables which are to be chosen such that a given cost function is minimized. For the continuous inequality constraints on the state, we construct approximating smooth functions in integral form. Then, the summation of these approximating smooth functions in integral form, which is called the constraint violation, is appended to the cost function to form a new augmented cost function. In this way, we obtain a sequence of approximate optimization problems subject to only boundedness constraints on the decision variables. Then, the gradient of the augmented cost function is derived. On this basis, we develop an effective computational method for solving the time-delay optimal control problem with continuous inequality constraints on the state and control via solving a sequence of approximate optimization problems, each of which can be solved as a nonlinear optimization problem by using existing gradient-based optimization techniques. This proposed method is then used to solve a practical optimal control problem arising in the study of a real evaporation process. The results obtained are highly satisfactory, showing that the proposed method is highly effective.The fourth problem that we consider is a max-min optimal control problem arising in the study of gradient elution chromatography, where the manipulative variables in the chromatographic process are to be chosen such that the separation efficiency is maximized. This problem has three non-standard characteristics: (i) The objective function is nonsmooth; (ii) each state variable is defined over a different time horizon; and (iii) the order of the final times for the state variable, the so-called retention times, are not fixed. To solve this problem, we first introduce a set of auxiliary decision variables to govern the ordering of the retention times. The integer constraints on these auxiliary decision variables are approximated by continuous boundedness constraints. Then, we approximate the control by a piecewise constant function, and apply a novel time-scaling transformation to map the retention times and control switching times to fixed points in a new time horizon. The retention times and control switching times become decision variables in the new time horizon. In addition, the max-min objective function is approximated by a minimization problem subject to an additional constraint. On this basis, the optimal control problem is reduced to an approximate nonlinear optimization problem subject to smooth constraints, which is then solved using a recently developed exact penalty function method. Numerical results obtained show that this approach is highly effective.Finally, some concluding remarks and suggestions for further study are made in the conclusion chapter.