Trading a mean-reverting asset: Buy low and sell high

This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two quasi-algebraic equations. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results.     

On a system of first-order quasi-variational inequalities connected with the optimal switching problem

In this paper we prove the existence of the maximum bounded Lipschitz continuous solution to a system of first-order quasi-variational inequalities. The method is to discretize by an Euler scheme the characteristic lines of the differential operator appearing in the system and to solve by iteration the corresponding approximate problem. The solution is interpreted as the value function of a deterministic optimal switching problem.     

On optimal control of a brownian motion

This paper is concerned with the optimal control of a Brownian motion on R⁺. The process is controlled by switching control action to affect the variance and the drift. There is a cost which depends on the state of the process and the action used to operate the system. There is another cost incurred instantaneously to switch the control action. A quasi-variational inequality is solved as the dynamic programming equation for a long run average cost criterion.     

An optimal stopping time problem with time average cost in a bounded interval

An optimal stopping time problem for a diffusion process stopped at the boundary of a bounded interval is studied. Our cost functional is of time average type which is different from standard long term average cost functional but can be considered as a version of the Gittins index. Both characterization of the, value function and construction of optimal stopping policy will be presented.     

Approximations for optimal stopping of a piecewise-deterministic process

This paper deals with approximation techniques for the optimal stopping of a piecewise-deterministic Markov process (P.D.P.). Such processes consist of a mixture of deterministic motion and random jumps. In the first part of the paper (Section 3) we study the optimal stopping problem with lower semianalytic gain function; our main result is the construction of ε-optimal stopping times. In the second part (Section 4) we consider a P.D.P. satisfying some smoothness conditions, and forN integer we construct a discretized P.D.P. which retains the main characteristics of the original process. By iterations of the single jump operator from ℝ ^N to ℝ ^N , each iteration consisting ofN one-dimensional minimizations, we can calculate the payoff function of the discretized process. We demonstrate the convergence of the payoff functions, and for the case when the state space is compact we construct ε-optimal stopping times for the original problem using the payoff function of the discretized problem. A numerical example is presented.     

An optimal control approach to the optical flow problem

The optical flow problem is reduced to an optimal control problem governed by a linear parabolic equation having the unknown velocity field (the optical flow) as drift term. This model is derived from a new assumption, that is, the brightness intensity is conserved on a moving pattern driven by a Gaussian stochastic process. The optimality conditions are deduced by a passage to the limit technique in an approximating optimal control problem introduced for a regularization purpose. Finally, the controller uniqueness is addressed.     

An optimal control based approach to designing plantwide control system architectures

An approach to designing decentralized plantwide control system architectures is presented. The approach is based on splitting the optimal controller gain matrix that results from solving an output optimal control problem into feedback and feedforward parts. These two parts are then used to design and evaluate decentralized control systems. Results for the application of the methodology to a realistic, 4 by 4 reactor with recycle process are given. For this system, the optimal control based approach suggests feedback pairings that are significantly different than those suggested by the steady state RGA. The approach presented can give an indication if MPC is preferred over a decentralized approach to plantwide control. Comparison of the results produced by the best decentralized plantwide system and a model predictive control system are presented.     

带技术投资的保险公司最优策略

本文站在保险公司的角度,假定1)保险公司采用连续比例再保险的方式将自身的部分风险转移到再保险公司,2)保险公司可以选择在某一时刻进行项目投资,该投资不直接产生收益,但可以降低公司所面临的风险.本文的目标是通过选择最佳投资时刻和最优再保险比例来最小化破产概率.运用混合随机决策–最优停时方法,本文求解出破产概率和最优再保险策略的显式表达式以及最佳投资时刻的半显式解.作为本文结果的一个应用,本文以数值模拟的方式揭示了投资效果,投资金额和最佳投资时刻3者之间的关系:1)投资总是可以降低破产概率;2)投资效果越明显,投资所需金额越小,则应该选择尽早投资;反之则应该推迟投资时间,等积累到足够的资金再进行投资.     

Partially observed non-linear risk-sensitive optimal stopping control for non-linear discrete-time systems

In this paper we introduce and solve the partially observed optimal stopping non-linear risk-sensitive stochastic control problem for discrete-time non-linear systems. The presented results are closely related to previous results for finite horizon partially observed risk-sensitive stochastic control problem. An information state approach is used and a new (three-way) separation principle established that leads to a forward dynamic programming equation and a backward dynamic programming inequality equation (both infinite dimensional). A verification theorem is given that establishes the optimal control and optimal stopping time. The risk-neutral optimal stopping stochastic control problem is also discussed.     

Robust optimal control of bilinear DC-DC converters

This paper addresses the control problem of dc-dc converters. The control law synthesis considered here exploits the potential of LMI-based control approaches, which allow to cope with model uncertainty, disturbances and bilinearities to synthesize simple state-feedback controllers with a priori guarantee of stability in a large domain of initial and operating conditions. The aim of the paper is to contribute with a robust control framework to deal with the common requirements of regulated dc-dc converters. The correctness of the results has been verified both with numerical simulations and with experimental measurements from a laboratory prototype.     

偏微分方程图像平滑模型的一种最优停止准则

基于偏微分方程的各种非线性图像平滑模型, 可归结为求解初始值为输入图像的非线性扩散方程. 这些非线性图像平滑模型在滤除噪声的同时, 在保留图像重要特征方面表现出良好的性能.采用这些模型对图像进行平滑的过程中,迭代停止准则对图像平滑的效果有着重要的影响.该文提出了一种简单实用的最优停止准则,该准则确定了一个标准,使得平滑后的图像与噪声的相关性最小时停止迭代. 它易于实现而且又有很强的通用性.实验结果表明该算法可以在图像平滑过程中适时地停止迭代, 获得满意的图像平滑效果.     

Time series regression-based pairs trading in the Korean equities market

Abstract

Pairs trading is an instance of statistical arbitrage that relies on heavy quantitative data analysis to profit by capitalising low-risk trading opportunities provided by anomalies of related assets. A key element in pairs trading is the rule by which open and close trading triggers are defined. This paper investigates the use of time series regression to define the rule which has previously been identified with fixed threshold-based approaches. Empirical results indicate that our approach may yield significantly increased excess returns compared to ones obtained by previous approaches on large capitalisation stocks in the Korean equities market.     

A trend-following strategy: Conditions for optimality

Based on trend-following trading strategies that are widely used in the investment world, this work provides a set of sufficient conditions that determine the optimality of the traditional trend-following strategies when the trends are completely observable. A dynamic programming approach is used to verify the optimality under these conditions. The value functions are characterized by the associated HJB equations, and are shown to be either linear functions or infinity depending on the parameter values. The results reveal two counterintuitive facts: (a) trend following may not lead to optimal reward in some cases even when/if the investor knows exactly when a trend change occurs; (b) stock volatility is not relevant in trend following when trends are observable.     

Modeling the dynamic optimal advertising in stochastic condition

An effort to model the dynamic optimal advertising was made with the uncertainty of sales responses in consideration. The problem of dynamic advertising was depicted as a Markov decision process with two state variables. When a firm launches an advertising campaign, it may predict the probability that the campaign will obtain the sales reponse. This probability was chosen as one state variable. Cumulative sales volume was chosen as another state variable which varies randomly with advertising. The only decision variable was advertising expenditure. With these variables, a multi-stage Markov decision process model was formulated. On the basis of some propositions the model was analyzed. Some analytical results about the optimal strategy have been derived, and their practical implications have been explained.     

An optimal control for a flotation circuit

The optimal operation of a flotation circuit, which is used to separate two minerals is discussed. The optimal control of the flotation circuit at Lake Dufault is found to be a bang-bang control, to contain a singular sub-arc, or to be totally singular depending on the various practical constraints. The influence of the time-delay on the optimal control of the flotation circuit is then investigated. Although the influence of the delay is quite significant, the basic structure of the optimal policy remains roughly the same. Thus it is not unreasonable to ignore the delay, although the optimality suffers from this.     

Some new error inequalities for a generalized quadrature rule of open type

Some new error inequalities for a generalized quadrature rule of open type are established. Especially, two sharp inequalities are derived when n is an odd and an even integer, respectively.     

An optimal layout methodology for cold forming rectangular parts using genetic algorithms

Cold forming is widely used in manufacturing processing, and the layout of rectangular parts in the strip is manually accomplished, which is a time-consuming task and may be a major bottleneck in effectively improving the utilization ratio of material and the productivity. The mathematical model for optimal layout of cold forming is first developed, and then the constrained optimal layout problem is transformed to an unconstrained optimal one with penalty function strategy. A simple genetic algorithms for this optimal layout is proposed, and an example is examined to show the validity of this proposed genetic methodology. Although the simple genetic algorithms is employed, a higher material utilization ratio and productivity is achieved.     

An optimal motion planning method for computer-assisted surgical training

This paper focuses on the development and validation of an optimal motion planning method for computer-assisted surgical training. The context of this work is the development of new-generation systems that combine artificial intelligence and computer vision techniques in order to adjust the learning process to specific needs of a trainee, while preventing a trainee from the memorization of particular task settings. The problem described in the paper is the generation of shortest, collision-free trajectories for laparoscopic instrument movements in the rigid block world used for hand–eye coordination tasks. Optimal trajectories are displayed on a monitor to provide continuous visual guidance for optimal navigation of instruments. The key result of the work is a framework for the transition from surgical training systems in which users are dependent on predefined task settings and lack guidance for optimal navigation of laparoscopic instruments, to the so called intelligent systems that can potentially deliver the utmost flexibility to the learning process. A preliminary empirical evaluation of the developed optimal motion planning method has demonstrated the increase of total scores measured by total time taken to complete the task, and the instrument movement economy ratio. Experimentation with different task settings and the technical enhancement of the visual guidance are subjects of future research.