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Notes
1 Note that beyond this classical implication of the EMH, other theoretical research also suggests that prices may well be extremely hard to predict Bouchaud et al. (Citation2004).
Lo (Citation2004) referred to the Adaptive Market Hypothesis instead of EMH.
Brandouy et al. (Citation2009) give concrete examples of buying all and selling all trading rules described in this section.
There is no restriction on the nature of the risky asset A, which can be a stock, a portfolio or a market index. We posit a price-taker framework, i.e., investors’ decisions cannot affect these prices and sufficient liquidity at these prices is assumed.
denotes the set of all rational numbers.
Throughout this article, except if specifically indicated, will always denote the binary logarithm.
In our example, the is added by ‘1’ at each time
increases. As
, this difference - although tending to
with
- cannot modify the limit mean of
.
Differences between these cases are described in the figure comments
A short presentation of geometric strategies is given in Appendix B.
Zenil and Delahaye (Citation2011) propose a general investigation on this subject.
Their definition was first proposed by Martin-Löf
In this paper, a random variable is
if
,
et
.