Quantitative finance formular are mostly based on martingales, Poisson jump, GBM, CEV, etc.. The logic behind it is that martingale means the future could not be predicted, or, EMH (Efficient-market hypothesis).

fair enough. however, EMH is only a hypothesis now, the other side of the story, that the market is inefficient, could also stands -- provided the inefficiency is always found and exploited then disappeared.

so, is there some theory / math model, that is based on non-martingale analysis?


1 Answer 1


In the equilibrium models you can assume that there exists so called Alpha, i.e. an opportunity that can be exploited. Most of the buy side models (i.e. asset allocation, portfolio construction) are based on this idea.

As a theoretical model, you can consider CAPM with heterogeneous beliefs:

Hedge funds claim to generate the “Alpha”, i.e., excess returns that cannot be explained by market risk. ... The assumption of homogeneous beliefs was always under scrutiny among finance theorists. Removing it we can model the Alpha within the CAPM, i.e., as a property of financial market equilibria! We show that in a CAPM with heterogeneous beliefs every investor who holds beliefs different to the average market belief, sees some Alpha.

from Financial Economics: A Concise Introduction to Classical and Behavioral Finance

In the long-run the outcome of this model is consistent with the efficient market hypothesis and also with the CAPM based on homogeneous beliefs, i.e. Alpha diminishes.


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