Convergence Rate, Chebyshev's Inequality, and Financial Policy

收歛率、謝氏雪夫不等式和融資策略

10.6226/NTURM2000.10.2.97

謝世佳(Hsih-Chia Hsieh)

Bellman方程式 ； 二次動態迴歸分析 ； 最適均衡 ； Multivariate optimum equilibrium ； Games ； Sampling ； Invariance, Nonlinearity ； Sequential quality control ； Weighted least squares. Without iteration

臺大管理論叢

10卷2期（2000 / 06 / 01）

97 - 133

英文

本研究利用動態兩次迴歸，求解多目標的規劃，提出均衡策略，並檢定異常的狀態。 例如，本研究分析旅遊電子商務的經濟效益，利用高頻率的資料。使用動態二次模型，來分析廠商和旅行社之進入和退出旅遊電子商務。電子商務促進旅遊次數，增加利潤和就業。減少旅遊的費用支出。淨效用是增加旅行社的收入和利潤。 本研究方法是動態二次分析的迴歸，用於最適控制電子商務，分配促銷的經費，藉以增加電子商務的業務。政策含意是，旅遊商業公會和消費者保護公會須致力維護電子商務的信譽。 本研究有利於學生學習電子商務的迴歸分析。最適控制的迴歸分析可廣泛用於其他科學領域。

This paper applies the dynamic quadratic regression for global optimization and provides a global convergence theory. It tests the probability p value of the convergence to the global optimum under the time-invariant policy rule. Its nonlinear optimization does imply the existence of a stable solution. A new test of p values supplements the F, Student t and Neyman's test statistics for the stable region, which otherwise vary with time or sample sizes and are not robust to abnormality. The original model is approximated by a smooth and strictly concave differential equation. It is approximated by an improved logistic quadratic regression, which solves the second-order differential equation and refines Chebyshev's inequality. It detects the deviation of the sample mean from the fixed point. With either no iterations or a small number of iterations, this algorithm outperforms most other iterative algorithms for some class of optimization problems. The nonlinear system is indefinite in sign. It is solved as a switching model. Around this turning point, the feedback rule has parameters systematically altering in sign. Using seven theorems, it proves that x(superscript *) is the primary solution of (The equation is abbreviated) and denotes the multivariate optimum equilibrium. It illustrate the sequential quality control and the predator-prey models.

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