Time-consistent asymptotic exponential arbitrage with small probable maximum loss. (English) Zbl 1417.91464
Summary: Based on a concept of asymptotic exponential arbitrage proposed by H. Föllmer and W. Schachermayer [Math. Financ. Econ. 1, No. 3–4, 213–249 (2008; Zbl 1153.91015)], the author introduces a new formulation of asymptotic arbitrage with two main differences from the previous one: Firstly, the realising strategy does not depend on the maturity time while the previous one does, and secondly, the probable maximum loss is allowed to be small constant instead of a decreasing function of time. The main result gives a sufficient condition on stock prices for the existence of such asymptotic arbitrage. As a consequence, she gives a new proof of a conjecture of Föllmer and Schachermayer.
MSC:
| 91G10 | Portfolio theory |
Citations:
Zbl 1153.91015References:
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| [3] | Föllmer, H. and Schachermayer, W., Asymptotic arbitrage and large deviations, Mathematics and Financial Economics, 1(3-4), 2008, 213-249. · Zbl 1153.91015 · doi:10.1007/s11579-008-0009-3 |
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