定理5.1的两个相关引理及它们的各自贡献论文_代维,杨丰瑞

（1湖北农谷实业集团有限责任公司 湖北荆门 431821；2重庆邮电大学 重庆 400000）

摘要：本文通过利用泰勒微分展开式和维纳过程相关数学特性，成功阐述了弗里德曼《随机微分方程及应用》一书第80页的定理5.1的证明过程。同时由此展开，延伸证明了两个引理并阐述了两个引理的各自相关贡献。

关键词：维纳过程；泰勒展开式；随机微分方程；引理

[Abstract] This paper sets out the proof process of theorem5.1 quoted from Page 80 of Stochastic Differential Equations And Applications by Avner Friedman, mainly utilizing Taylor expansion equation and some Wiener process characteristics. In the part ensuing, the paper extends the deduction to reach two lemmas, the respective contribution of which to the APT model in finance and the existing advanced mathematics have been elaborated.

[Keywords] Wiener process;Taylor expansion equation; stochastic differential equation; lemma

Avner Friedman gives out Theorem 5.1 in the book Stochastic Differential Equations and Applications on page 80. It states as follows:

Proof of lemma2 is completed.

Remark

This paper originates from the theorem5.1 Avner mentioned in his special work and extends the theorem to reach two lemmas. The more complicated the G function form in the paper, the more will do the corresponding conclusion deduction process. For lemma1, it actually iterates what the aggregate function’s incremental behavior will be like when its factors are simultaneously multiplied together other than simple addition. Like the APT (Arbitrage Pricing Theory) model in finance, where it treats factors affecting the return rate of the asset conjunct with additive and assume the factors are certain. However this article here firstly extends the assumption of factors to be stochastic, containing drift and disturbance item; second, the factors are organized by multiplication rather than additive. From the two perspectives above, we can extend the APT model to be more complicated and more analogous to the true reality which can of course at any time be only approximated and never be completely simulated. Limited to the author’s academic level, the paper doesn’t roll out the extensive deduction anymore, which will also demonstrate a field deserving research in the future. However, lemma1 can be utilized to enrich and develop APT model and as such similar ones in the corresponding field, which is irrefutable. For Lemma2, this article for the first time works out the derivative formula for the division between two functions whose behavior has been expanded to be stochastic, which is a contribution to the existing advanced mathematics.

Reference：

[1]Avner Friedman, Stochastic Differential Equations And Applications[J],1975-1976:80-80;

[2] Jonathan E.Ingersoll.Jr., Theory of Financial Decision Making[J], 2008:330-332;

[3] N.H.Chanand H.Y. Wong, HANDBOOK OF FINANCIAL RISK MANAGEMENT simulations and Case Studies[J], 2016.8:38-39.

作者简介：代维，湖北农谷实业集团有限责任公司资本营运中心副主任，重庆邮电大学管理科学与工程专业硕士。

杨丰瑞，重庆邮电大学经济管理学院教授，四川大学政治经济学院博士。同时任重庆重邮信科集团股份有限公司董事长（2019年3月任期结束）。

论文作者:代维,杨丰瑞

论文发表刊物:《科技研究》2019年3期

论文发表时间:2019/6/10

标签：重庆论文;  泰勒论文;  湖北论文;  微分方程论文;  有限责任公司论文;  邮电大学论文;  定理论文;  《科技研究》2019年3期论文;