Wrong Use of Averages Implies Wrong Results from Many Heuristic Models

• 作者: Galiya Klinkova Michael Grabinski
• 来源期刊: 应用数学(英文)
• 学科: 医学
• 关键词: Mean MEDIAN CHAOS FINANCE Random Fractals
• 年，卷（期）: 2019,（7）
• 页码范围: 605-618
• 页数: 14页
• 分类号: R73

摘要

In a linear world, averages make perfect sense. Something too big is compensated by something too small. We show, however that the underlying differential equations (e.g. unlimited growth) rather than the equations themselves (e.g. exponential growth) need to be linear. Especially in finance and economics non-linear differential equations are used although the input parameters are average quantities (e.g. average spending). It leads to the sad conclusion that almost all results are at least doubtful. Within one model (diffusion model of marketing) we show that the error is tremendous. We also compare chaotic results to random ones. Though these data are hardly distinguishable, certain limits prove to be very different. Implications for finance can be important because e.g. stock prices vary generally, chaotically, though the evaluation assumes quite often randomness.