Abstract
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.
Highlights
IntroductionAlmost everybody knows how to calculate an average or (arithmetic) mean, and its use is widespread
Almost everybody knows how to calculate an average or mean, and its use is widespread
In finance and economics non-linear differential equations are used the input parameters are average quantities
Summary
Almost everybody knows how to calculate an average or (arithmetic) mean, and its use is widespread. For “does not fit”, it is irrelevant whether the screw is too small or too big Speaking such a use-function must be strictly linear. Nobody doubts that the financial word is governed by non-linear differential equations If it was not, the solutions would have to be plane waves in contrast to all observations. It is due to the fact that typical financial data such as e.g. stock prices are, unlike the market share, not conserved This led to the suggestion of a conserved value [5] in finance. Building arithmetic means in chaotically varying quantities sometimes (but not always) gives identical results to random variations as one might expect Is a statistical analysis allowed at all? Can one modify ordinary statistics in order to cope with it?
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