保险是一个遍历性问题

IF 1.5 Q3 BUSINESS, FINANCE
O. Peters
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引用次数: 0

摘要

2014年11月,经济学家肯·阿罗(Ken Arrow)和我就我从遍历性问题的角度重新构想经济科学的努力进行了一次长谈(Peters, 2019)。在经济学中,遍历性是关于处理随机性的两种不同的平均方法。假设我们在规则间隔时间t = 1处测量某个量…T,并将其建模为随机过程x(T,ω),其中ω表示该过程的实现。如果我们想将过程简化为单个信息数,我们可以对实现集合进行平均,得到期望值E [x] (t)= limN→∞1 N∑N i x(t,ωi),或者我们可以对时间进行平均,得到时间平均值t [x] (ω)= limT→∞1 t∑t x(t,ωi),如图1所示。如果过程是遍历的,那么两种平均方法将得到相同的结果。我们感兴趣的是它不成立的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Insurance as an ergodicity problem
In November 2014, the economist Ken Arrow and I had one of our long conversations about my efforts to re-imagine economic science from the perspective of the ergodicity problem (Peters, 2019). Ergodicity, as it pertains to economics, is about two different ways of averaging to deal with randomness. Let us say we measure some quantity at regularly spaced times t = 1 . . . T and model it as a stochastic process, x(t,ω), where ω denotes the realization of the process. If we want to reduce the process to a single informative number, we can average across the ensemble of realizations, yielding the expected value E [x] (t)= limN→∞ 1 N ∑N i x(t,ωi), or we can average across time, yielding the time average T [x] (ω)= limT→∞ 1 T ∑T t x(t,ωi), Fig. 1. If the process is ergodic, then the two ways of averaging will give the same result. We are interested in cases where this is not true.
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来源期刊
CiteScore
3.10
自引率
5.90%
发文量
22
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