Government Debt, Budget Surplus, and Popularity of Politicians

This paper sets up a positive model of government behavior to determine the optimal fiscal policy of a politician who aims to reach a certain target level of national debt and remain popular at the same time. We model explicitly the response of the citizens to the fiscal policy set by the politician. To that end, we assume that citizens form an equilibrium acceptance rate of savings and adjust dynamically this savings rate to the currently prevailing levels of government debt and primary surplus. The difference between the equilibrium acceptance rate of savings as formed by the public and the fiscal policy actually chosen by the politician determines the politician popularity. Using the Pontryagin maximum principle, we derive the optimal level of the fiscal policy and investigate its local stability depending on the parameters of the model. We show that cyclical strategies [that is, phases of saving (primary surplus) and spending (primary deficit)], may be optimal.     

A multi-objective multi-period stochastic programming model for public debt management

While raising debt on behalf of the government, public debt managers need to consider several possibly conflicting objectives and have to find an appropriate combination for government debt taking into account the uncertainty with regard to the future state of the economy. In this paper, we explicitly consider the underlying uncertainties with a complex multi-period stochastic programming model that captures the trade-offs between the objectives. The model is designed to aid the decision makers in formulating the debt issuance strategy. We apply an interactive procedure that guides the issuer to identify good strategies and demonstrate this approach for the public debt management problem of Turkey.     

Budget balancing in a two-dimensional macroeconomic model

A two-person nonlinear dynamic game is presented to model the government's strategy to decrease the budget deficit, where Player 1 is the government using fiscal control and Player 2 represents the private sector. In our macroeconomic model the growth rate of the labour force is not known, but its lower and upper bounds are given a priori. This means that the system is uncertain, which makes the determination of an optimal solution (in a Nash, Stackelberg, etc. sense) impossible. Therefore, only a guaranteeing cost control is determined for Player 1. It is shown that the balancing by a guaranteeing cost control is possible even in the most unfavourable situation, when the governmental debt is higher and the volume of fixed capital stock is lower than the equilibrium value.     

Optimal control problem for an insurance surplus model with debt liability

For an insurance company with a debt liability, they could make some management actions, such as reinsurance, paying dividends, and capital injection, to balance the profitability and financial bankruptcy. Our objective is to determine risk retention rate, dividend, and capital injection strategy so as to maximize the expected discounted dividends minus the discounted cost of capital injection until the time of ruin. We assume that the dividend payments and capital injection should occur with both fixed and proportional costs. We obtain explicit expressions of the optimal value functions as well as the corresponding optimal joint strategies by routine procedures in a comprehensive basic model using a new technique to solve the related equations. Our results show that whether recapitalizing is profitable or not depends on the costs of capital raising and that the firm injects capital only when the reserves are zero and recapitalizes to the optimal reserves level if the cost of external capital is low. Copyright © 2013 John Wiley & Sons, Ltd.     

Impulse Control of One-Dimensional Ito Diffusions with an Expected and a Pathwise Ergodic Criterion

We consider the problem of controlling a general one-dimensional Ito diffusion by means of an impulse control process. The objective is to minimise a long-term expected criterion as well as a long-term pathwise criterion that penalise both deviations of the state process from a given nominal point and the use of impulsive control effort. In particular, each time the controller deploys an impulse to reposition the system's state, a fixed cost and a cost proportional to the impulse's size are incurred. We solve the resulting optimisation problems and we provide an explicit characterisation of an optimal control strategy under general assumptions. The control of a foreign exchange rate or an inflation rate presents a potential application of the model that we study.     

A Markov decision problem in a risk model with interest rate and Markovian environment

We consider the compound binomial model in a Markovian environment presented by Cossette et al.(2004). We modify the model via assuming that the company receives interest on the surplus and a positive real-valued premium per unit time, and introducing a control strategy of periodic dividend payments. A Markov decision problem arises and the control objective is to maximize the cumulative expected discounted dividends paid to the shareholders until ruin minus a discounted penalty for ruin. We show that under the absence of a ceiling of dividend rates the optimal strategy is a conditional band strategy given the current state of the environment process. Under the presence of a ceiling for dividend rates, the character of the optimal control strategy is given. In addition, we offer an algorithm for the optimal strategy and the optimal value function.Numerical results are provided to illustrate the algorithm and the impact of the penalty.     

Dial-Up Internet Access: A Two-Provider Cost Model

We present a cost model for splitting Internet dial-up traffic (which varies by time-of-day) between two large modem banks. One of the modem banks charges by the hour, the other charges for the peak number-in-system during the day. To study if the possible savings are enough to make the effort worthwhile, we formulate a clairvoyant (“perfect information”) Integer Program that is equivalent to a network flow problem. This leads us to use a ceiling policy. In the stochastic control case, we use a Modified Offered Load (MOL) approximation to explore the properties of the system, and develop a square-root-type rule to set the ceiling in the homogeneous case. We also use simulation to determine an optimal ceiling when we cannot route individual calls precisely. We propose approximations that may be computed for any call duration distribution, and compare their answers to exact differential-equation procedures for Exponential call durations. AMS subject classification: 60K25, 90B18, 68M20, 90B22, 60K30     

Approximation of Markov decision processes with general state space

We deal with a discrete-time finite horizon Markov decision process with locally compact Borel state and action spaces, and possibly unbounded cost function. Based on Lipschitz continuity of the elements of the control model, we propose a state and action discretization procedure for approximating the optimal value function and an optimal policy of the original control model. We provide explicit bounds on the approximation errors. Our results are illustrated by a numerical application to a fisheries management problem.     

Geometric Kinematic Control of a Spherical Rolling Robot

We give a geometric account of kinematic control of a spherical rolling robot controlled by two internal wheels just like the toy robot Sphero. Particularly, we introduce the notion of shape space and fibers to the system by exploiting its symmetry and the principal bundle structure of its configuration space; the shape space encodes the rotational angles of the wheels, whereas each fiber encodes the translational and rotational configurations of the robot for a particular shape. We show that the system is fiber controllable—meaning any translational and rotational configuration modulo shapes is reachable—as well as find exact expressions of the geometric phase or holonomy under some particular controls. We also solve an optimal control problem of the spherical robot, show that it is completely integrable, and find an explicit solution of the problem.     

A continuous-time search model with job switch and jumps

We study a new search problem in continuous time. In the traditional approach, the basic formulation is to maximize the expected (discounted) return obtained by taking a job, net of search cost incurred until the job is taken. Implicitly assumed in the traditional modeling is that the agent has no job at all during the search period or her decision on a new job is independent of the job situation she is currently engaged in. In contrast, we incorporate the fact that the agent has a job currently and starts searching a new job. Hence we can handle more realistic situation of the search problem. We provide optimal decision rules as to both quitting the current job and taking a new job as well as explicit solutions and proofs of optimality. Further, we extend to a situation where the agent’s current job satisfaction may be affected by sudden downward jumps (e.g., de-motivating events), where we also find an explicit solution; it is rather a rare case that one finds explicit solutions in control problems using a jump diffusion.     

公共资产预算配置的拍卖机制设计

本文探讨在财政部门作为政府出资人的框架下,通过设计一套可行的竞标机制来提高预算项目的配置效率。结合运用机制设计理论和拍卖理论与方法建立竞标机制设计模型,在保证竞标预算单位参与投标和真实显示自己效率的条件下最大化拍卖者——政府出资人的期望效用,并通过求解此模型得到最优的竞标机制。鉴于最优机制在形式上的复杂性,给出了第二高得分拍卖这种最优拍卖方式。最后对公共资产配置预算的规则如何确定才能减少效率损失进行了归纳。     

Optimal control of a finite dam with a sample path constraint

In this paper, we discuss the 2-stage output procedure of a finite dam under the condition that water must be released by a fixed time. From this standpoint, the reservoir model we consider is subject to a sample path constraint and has a more general cost function than the earlier contributions. We analytically derive explicit formulas for the long-run average and the expected total discounted costs for an infinite time span and numerically calculate the optimal control policy. Finally, the optimal policy is compared with one by Zuckerman [1] and the effect of the fixed release time is discussed further.     

A boundary control problem for the blood flow in venous insufficiency. The general case

The purpose of this article is to introduce and study an optimal control problem with medical applications. When a vein loses its elasticity, phenomena such as stagnation and recirculation of the blood may appear; these phenomena produce medical complications. We propose an optimization model in order to diminish the negative consequences of the lack of vein elasticity. We extend a previous model involving the interaction between a viscous fluid and an elastic boundary to the case when both the fluid and the elastic medium occupy three dimensional domains. After establishing the existence and uniqueness of the solution for the coupled problem, we present a boundary control problem in order to determine an exterior compression that realizes a blood flow without recirculation. Since it is not possible to find such a compression directly, we consider a sequence of cost functionals and we study the corresponding optimal control problems. The existence and uniqueness of the optimal controls are proved and the optimality conditions that characterize the optimal controls are derived. Finally, we establish the relation between the control problem with physical meaning and the sequence of optimal controls already constructed.     

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.     

A Transformation Approach in Shape Optimization: Existence and Regularity Results

In this article, we consider a model shape optimization problem. The state variable solves an elliptic equation on a star-shaped domain, where the radius is given via a control function. First, we reformulate the problem on a fixed reference domain, where we focus on the regularity needed to ensure the existence of an optimal solution. Second, we introduce the Lagrangian and use it to show that the optimal solution possesses a higher regularity, which allows for the explicit computation of the derivative of the reduced cost functional as a boundary integral. We finish the article with some second-order optimality conditions.     

A mixed integer linear programming model for optimal sovereign debt issuance

Governments borrow funds to finance the excess of cash payments or interest payments over receipts, usually by issuing fixed income debt and index-linked debt. The goal of this work is to propose a stochastic optimization-based approach to determine the composition of the portfolio issued over a series of government auctions for the fixed income debt, to minimize the cost of servicing debt while controlling risk and maintaining market liquidity. We show that this debt issuance problem can be modeled as a mixed integer linear programming problem with a receding horizon. The stochastic model for the interest rates is calibrated using a Kalman filter and the future interest rates are represented using a recombining trinomial lattice for the purpose of scenario-based optimization. The use of a latent factor interest rate model and a recombining lattice provides us with a realistic, yet very tractable scenario generator and allows us to do a multi-stage stochastic optimization involving integer variables on an ordinary desktop in a matter of seconds. This, in turn, facilitates frequent re-calibration of the interest rate model and re-optimization of the issuance throughout the budgetary year allows us to respond to the changes in the interest rate environment. We successfully demonstrate the utility of our approach by out-of-sample back-testing on the UK debt issuance data.     

A controllable linear stochastic system with delay in the information feedback channel

We consider the problem of optimal control of the solution of a linear stochastic differential equation whose stochastic terms depend on the solution and a control in the presence of variable delay in the information feedback channel. We find an explicit form for the optimal control minimizing a quadratic cost functional.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 37–43, 1986.     

Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic

We address a rate control problem associated with a single server Markovian queueing system with customer abandonment in heavy traffic. The controller can choose a buffer size for the queueing system and also can dynamically control the service rate (equivalently the arrival rate) depending on the current state of the system. An infinite horizon cost minimization problem is considered here. The cost function includes a penalty for each rejected customer, a control cost related to the adjustment of the service rate and a penalty for each abandoning customer. We obtain an explicit optimal strategy for the limiting diffusion control problem (the Brownian control problem or BCP) which consists of a threshold-type optimal rejection process and a feedback-type optimal drift control. This solution is then used to construct an asymptotically optimal control policy, i.e. an optimal buffer size and an optimal service rate for the queueing system in heavy traffic. The properties of generalized regulator maps and weak convergence techniques are employed to prove the asymptotic optimality of this policy. In addition, we identify the parameter regimes where the infinite buffer size is optimal.     

OPTIMAL HARVESTING OF A SPATIALLY EXPLICIT FISHERY MODEL

Abstract We consider an optimal fishery harvesting problem using a spatially explicit model with a semilinear elliptic PDE, Dirichlet boundary conditions, and logistic population growth. We consider two objective functionals: maximizing the yield and minimizing the cost or the variation in the fishing effort (control). Existence, necessary conditions, and uniqueness for the optimal harvesting control for both cases are established. Results for maximizing the yield with Neumann (no‐flux) boundary conditions are also given. The optimal control when minimizing the variation is characterized by a variational inequality instead of the usual algebraic characterization, which involves the solutions of an optimality system of nonlinear elliptic partial differential equations. Numerical examples are given to illustrate the results.