Impact of correlated private signals on continuous-time insider trading

A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establish three lemmas:normal corre-lation,equivalent pricing and equivalent profit,which can guarantee to turn our model into a model with insider knowing full information.Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule.It shows that in the equilibrium,(1)the market depth is constant over time;(2)if the two noisy signals are not linerly correlated,then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end;(3)if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value,then our model turns into a model with insider knowing full information;(4)if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing,while down to O as the noise going up to infinity;(5)if the two noisy signals are not linear correlated then with one noisy signal fixed,the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value,and furthermore as the noisy value going to O it gets its maximum,the profit in the case that the real value is observed.

Parallel Control for Continuous-Time Linear Systems:A Case Study

In this paper,a new parallel controller is developed for continuous-time linear systems.The main contribution of the method is to establish a new parallel control law,where both state and control are considered as the input.The structure of the parallel control is provided,and the relationship between the parallel control and traditional feedback controls is presented.Considering the situations that the systems are controllable and incompletely controllable,the properties of the parallel control law are analyzed.The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable.Finally,numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method.Index Terms-Continuous-time linear systems,digital twin,parallel controller,parallel intelligence,parallel systems.

Identification of linear continuous-time system using wavelet modulating filters

An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable (Ⅳ) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

Continuous-time chaotic systems: Arbitrary full-state hybrid projective synchronization via a scalar signal

Relerrlng to contlnuous-Ume claaotlc systems, tills paper presents a new projective syncnromzatlon scheme, wnlcn enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic （hyperchaotic） systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.

Development of Optimal Maintenance Policies for Offshore Wind Turbine Gearboxes Based on the Non-homogeneous Continuous-Time Markov Process

Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.

Variance minimization for continuous-time Markov decision processes: two approaches

This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.

Enhanced LMI Representations for H2 Performance of Polytopic Uncertain Systems: Continuous-time Case

Based on two recent results, several new criteria of H2 performance for continuous-time linear systems are established by introducing two slack matrices. When used in robust analysis of systems with polytopic uncertainties, they can reduce conservatism inherent in the earlier quadratic method and the established parameter-dependent Lyapunov function approach. Two numerical examples are included to illustrate the feasibility and advantage of the proposed representations.

A continuous-time formulation for refinery production scheduling problems involving operational transitions in mode switching

In the refinery scheduling, operational transitions in mode switching are of great significance to formulate dynamic nature of production and obtain efficient schedules. The discrete-time formulation meets two main challenges in modeling: discrete approximation of time and large size of mixed-integer linear problem(MILP).In this article, a continuous-time refinery scheduling model, which involves transitions of mode switching, is presented due to these challenges. To reduce the difficulty in solving large scale MILPs resulting from the sequencing constraints, the global event-based formulation is chosen. Both transition constraints and production transitions are introduced and the numbers of key variables and constraints in both of the discrete-time and continuous-time formulations are analyzed and compared. Three cases with different lengths of time horizons and different numbers of orders are studied to show the efficiency of the proposed model.

Unbiased parameter estimation of continuous-time system based on modulating functions with input and output white noises

An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integration,an equivalent discrete identification model which is parameterized with continuous-time model parameters is developed,and the parameters can be estimated by the least-squares (LS) algorithm.Even with white noises in input and output measurement data,the LS estimate is biased,and the bias is determined by the variances of noises.According to the asymptotic analysis,the relationship between bias and noise variances is derived.One equation relating to the measurement noise variances is derived through the analysis of the LS errors.Increasing the degree of denominator of the system transfer function by one,an extended model is constructed.By comparing the true value and LS estimates of the parameters between original and extended model,another equation with input and output noise variances is formulated.So,the noise variances are resolved by the set of equations,the LS bias is eliminated and the unbiased estimates of system parameters are obtained.A simulation example by comparing the standard LS with bias eliminating LS algorithm indicates that the proposed algorithm is an efficient method with noisy input and output measurements.

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on compficated graphs. Using this method, we calculate the probability of Continuous-time classical and quantum random walks on many of finite direct product Cayley graphs （complete cycle, complete Kn, charter and n-cube）. Also, we inquire that the classical state the stationary uniform distribution is reached as t→∞ but for quantum state is not always satisfied.

A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

We develop an online adaptive dynamic programming （ADP） based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.

Hybrid Continuous-Time MILP Model for Crude Oil Scheduling under the Influence of High Tides

Vessels,especially very large or ultra large crude carriers(VLCCs or ULCCs),often can only dock and leave the berth during high tide periods to prevent being stranded.Unfortunately,the current crude scheduling models do not take into account tidal conditions,which will seriously affect the feasibility of crude schedule.So we first focus on the docking and leaving operations under the tidal actions,and establish a new hybrid continuous-time mixed integer linear programming(MILP)model which incorporates global event based formulation and unit-specific event based formulation.Upon considering that the multiple blending of crude oil can easily cause the production fluctuating,there are some reasonable assumptions that storage tanks can only store pure crude,and charging tanks just can be refilled after being emptied,which helps us obtain a simple MILP model without composition discrepancy caused by crude blending.Two cases are used to demonstrate the efficacy of proposed scheduling model.The results show that the optimization schedule can minimize the demurrage of the vessels and the number of feeding changeovers of crude oil distillation units(CDUs).

Robust Continuous-time Generalized Predictive Control for Large Time-delay System

A simple delay-predictive continuous-time generalized predictive controller with filter (F-SDCGPC) is proposed. By using modified predictive output signal and cost function, the delay compensator is incorporated in the control law with observer structure, and a filter is added for enhancing robustness. The design of filter does not affect the nominal set-point response, and it is more flexible than the design of observer polynomial. The analysis and simulation results show that the F-SDCGPC has better robustness than the observer structure without filter when large time-delay error is considered.

Identification of Continuous-Time Hammerstein System with Nuclear Norm Convex Relaxation

The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant( LTI) system and a static nonlinear function( the linear part is followed by the nonlinear part). The nonlinear function is approximated by the pseudospectral basis functions, which have a better performance than Hinge functions and Radial Basis functions. After the approximation on the nonlinear function, the CT Hammerstein system has been transformed into a multiple-input single-output( MISO) linear model system with the differential pre-filters. However, the coefficients of static nonlinearity and the numerators of the linear transfer function are coupled together to challenge the parameters identification of the Hammerstein system. This problem is solved by replacing the one-rank constraint of the regularization optimization with the nuclear norm convex relaxation. Finally, a numerical example is given to verify the accuracy and the efficiency of the method.

Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems

In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods.

Variance Optimization for Continuous-Time Markov Decision Processes

This paper considers the variance optimization problem of average reward in continuous-time Markov decision process (MDP). It is assumed that the state space is countable and the action space is Borel measurable space. The main purpose of this paper is to find the policy with the minimal variance in the deterministic stationary policy space. Unlike the traditional Markov decision process, the cost function in the variance criterion will be affected by future actions. To this end, we convert the variance minimization problem into a standard (MDP) by introducing a concept called pseudo-variance. Further, by giving the policy iterative algorithm of pseudo-variance optimization problem, the optimal policy of the original variance optimization problem is derived, and a sufficient condition for the variance optimal policy is given. Finally, we use an example to illustrate the conclusion of this paper.

Compressed Least Squares Algorithm of Continuous-Time Linear Stochastic Regression Model Using Sampling Data

In this paper,the authors consider a sparse parameter estimation problem in continuoustime linear stochastic regression models using sampling data.Based on the compressed sensing(CS)method,the authors propose a compressed least squares(LS) algorithm to deal with the challenges of parameter sparsity.At each sampling time instant,the proposed compressed LS algorithm first compresses the original high-dimensional regressor using a sensing matrix and obtains a low-dimensional LS estimate for the compressed unknown parameter.Then,the original high-dimensional sparse unknown parameter is recovered by a reconstruction method.By introducing a compressed excitation assumption and employing stochastic Lyapunov function and martingale estimate methods,the authors establish the performance analysis of the compressed LS algorithm under the condition on the sampling time interval without using independence or stationarity conditions on the system signals.At last,a simulation example is provided to verify the theoretical results by comparing the standard and the compressed LS algorithms for estimating a high-dimensional sparse unknown parameter.

Zero-Sum Continuous-Time Markov Games with One-Side Stopping

The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic programming principle reduces this problem to a system of ODEs with unilateral constraints.This system plays the role of the Bellman equation.We show that its solution provides the optimal strategies of the players.Additionally,the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints is derived.

Learning the continuous-time optimal decision law from discrete-time rewards

The concept of reward is fundamental in reinforcement learning with a wide range of applications in natural and social sciences.Seeking an interpretable reward for decision-making that largely shapes the system's behavior has always been a challenge in reinforcement learning.In this work,we explore a discrete-time reward for reinforcement learning in continuous time and action spaces that represent many phenomena captured by applying physical laws.We find that the discrete-time reward leads to the extraction of the unique continuous-time decision law and improved computational efficiency by dropping the integrator operator that appears in classical results with integral rewards.We apply this finding to solve output-feedback design problems in power systems.The results reveal that our approach removes an intermediate stage of identifying dynamical models.Our work suggests that the discrete-time reward is efficient in search of the desired decision law,which provides a computational tool to understand and modify the behavior of large-scale engineering systems using the optimal learned decision.