基于随机微分方程的易逝性高科技产品更新时机研究

Research on the renewal timing of perishable high-tech products based on stochastic differential equations

摘要:

科技的迅猛发展和消费者个性化的需求加速了易逝性高科技产品更新换代速度,导致易逝性高科技产品生命周期缩短,也随之引发创新不足的更新迭代问题。因此,本文基于易逝性高科技产品的价值易逝性与高新技术特性,构建了基于随机微分方程的易逝性高科技产品更新时机模型以解决易逝性高科技产品更新时机不确定性问题。首先,利用威布尔分布和多项式逼近函数构造无技术进步与价值易逝等外部因素干扰的易逝性高科技产品使用寿命模型；其次,采用布朗运动来模拟外部因素对易逝性高科技产品更新时机的影响情况,进而建立技术进步和价值易逝影响下易逝性高科技产品更新时机波动率模型；最后,选取iPad作为易逝性高科技产品案例验证本文所构建的易逝性高科技产品更新时机模型,研究结果表明该模型具有较强的稳健性,可为高新技术生产企业在产品更新换代时提供一定的参考。

关键词:随机微分方程;布朗运动;易逝性;高科技产品;更新时机

Abstract:

STheSrapid development of science and technology and the personalized demand of consumers have accelerated the replacement speed of perishable high-tech products, which has led to the shortening of the life cycle of perishable high-tech products and the problem of insufficient innovation in the renewal iteration. Therefore, this paperSconstructsSaSstochastic differential equation-based renewal timing model to solve the uncertainty of renewal timing of perishable high-tech products based on the value perishability and high-tech characteristics of perishable high-tech products. Firstly, the Weibull distribution and polynomial approximation function are used to construct a model of the service life of perishable high-tech products without the interference of external factors such as technological progress and value fallibility; Secondly, Brownian motion is used to simulate the influence of external factors on the renewal timing of perishable high-tech products, and then a volatility model of the renewal timing of perishable high-tech products under the influence of technological progress and value fallibility is established; Finally, iPad is selected as the case of fugitive high-tech products to verify the model of fugitive high-tech products" renewal timing constructed in this paper, and the research results show that the model has strong robustness and can provide some reference for high-tech manufacturers in product renewal.

Key words:stochastic differential equation; Brownian motion; fugacity; high-tech product; renewal timing