## Quelques remarques sur un théorème de Yan. (Some remarks on a theorem of Yan).(French)Zbl 0701.60041

Séminaire de probabilités XXIV 1988/89, Lect. Notes Math. 1426, 266-274 (1990).
[For the entire collection see Zbl 0695.00024.]
We begin with improving a theorem of J. Yan [Séminaire de Probabilités XIV, 1978/79, Lect. Notes Math. 784, 148-151 (1980; Zbl 0432.60071)] by extending it to spaces $$L^ p$$, $$1\leq p<+\infty$$. Thanks to this, the second author [Arbitrage et lois de martingale, Ann. Inst. Henri Poincaré 26, No.3, 451-460 (1990)] has recently shown the equivalence between the existence of a martingale law and the absence of free lunch. Then we prove that an admissible trading strategy for an agent $$\alpha_ 0$$ [according to D. Duffie and C. Huang’s definition, J. Math. Econ. 15, 283-303 (1986; Zbl 0608.90006)] is not generally admissible for an agent $$\alpha_ 1$$ even if $$\alpha_ 1$$ is better informed than $$\alpha_ 0.$$
Finally, we show that if there is no free lunch, classical hypothesis for economic models, this pathology doesn’t occur. This leads us to a detailed study of different notions of free lunch.
Reviewer: Jean-Pascal Ansel

### MSC:

 60G42 Martingales with discrete parameter

### Citations:

Zbl 0695.00024; Zbl 0432.60071; Zbl 0608.90006
Full Text: