Prediction and Optimization Performance Models for Poor Information Sample Prediction Problems

The prediction process often runs with small samples and under-sufficient information.To target this problem,we propose a performance comparison study that combines prediction and optimization algorithms based on experimental data analysis.Through a large number of prediction and optimization experiments,the accuracy and stability of the prediction method and the correction ability of the optimization method are studied.First,five traditional single-item prediction methods are used to process small samples with under-sufficient information,and the standard deviation method is used to assign weights on the five methods for combined forecasting.The accuracy of the prediction results is ranked.The mean and variance of the rankings reflect the accuracy and stability of the prediction method.Second,the error elimination prediction optimization method is proposed.To make,the prediction results are corrected by error elimination optimization method(EEOM),Markov optimization and two-layer optimization separately to obtain more accurate prediction results.The degree improvement and decline are used to reflect the correction ability of the optimization method.The results show that the accuracy and stability of combined prediction are the best in the prediction methods,and the correction ability of error elimination optimization is the best in the optimization methods.The combination of the two methods can well solve the problem of prediction with small samples and under-sufficient information.Finally,the accuracy of the combination of the combined prediction and the error elimination optimization is verified by predicting the number of unsafe events in civil aviation in a certain year.

OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION

This article is concerned with a class of control systems with Markovian switching, in which an It5 formula for Markov-modulated processes is derived. Moreover, an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman （HJB） equation with Markovian switching is characterized. Then, through the generalized HJB equation, we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation. Thus, we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds. Finally, for the CRRA utility function, we explicitly give the optimal consumption and portfolio policies. Numerical examples are included to illustrate the obtained results.

STRONG N-DISCOUNT AND FINITE-HORIZON OPTIMALITY FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES

This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish spaces.The corresponding transition rates are allowed to be unbounded,and the reward rates may have neither upper nor lower bounds.Under mild conditions,the authors prove the existence of strong n(n =—1,0)-discount optimal stationary policies by developing two equivalence relations:One is between the standard expected average reward and strong—1-discount optimality,and the other is between the bias and strong 0-discount optimality.The authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.

Theoretical search for solutions to minimize negative influence of segregation in mixing of particulate solids

The objective of this study is to examine several optimization problems in the batch mixing of segregating particulate solids that can be set up and solved using Markov chain models. To improve the adequacy of such models and exclude some physical contradictions that arise in the linear form, a non-linear Markov chain model for the mixing of segregating components is proposed. Optimal solutions are obtained by controlling the particle flow outside the mixing operating volume while the components are being loaded, modifying particle circulation inside the mixing zone during the process, and by structuring the load in the mixing zone. Solutions are found that not only reduce the negative influence of segregation, but also exclude it altogether. The gain resulting from optimization grows with the rate of segregation. The optimal solutions presented here can be used to improve the design of mixers.

OPTIMAL TRACKING FOR BILINEAR STOCHASTIC SYSTEM DRIVEN BY FRACTIONAL BROWNIAN MOTIONS

This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the solution to the equation are also studied.

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.