Abstract: In this chapter, the authors begin with some definitions applicable to positive continuous martingales in any martingale space. They apply the game-theoretic Girsanov theorem to obtain various continuous I-martingales that provide the basis for further discussion of the equity premium, capital asset pricing model (CAPM), and the theoretical performance deficit. The empirical study by Rajnish Mehra and Edward Prescott estimates the equity premium over the period 1889-2005 as 6.36%. The authors discuss implications of the game-theoretic CAPM for the Sharpe ratio, a standard performance measure for investment managers. The CAPM depends on a very different assumption from the standard CAPM, which is a result about equilibrium under rather unrealistic assumptions about the beliefs and preferences of participants in the market. The authors provide references to theoretical arguments for the existence of an efficient numeraire.
Publication Year: 2019
Publication Date: 2019-05-07
Language: en
Type: other
Indexed In: ['crossref']
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