Abstract
Suppose that a gambler places bets at discrete times t = 1,2,..., and that his fortune after the n’th bet is the random variable Xn. (Thus X 0 is the initial stake, and in general the Xn’s can take positive or negative real values.) How can we express the idea that the sequence of bets is “fair”?
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References
J. L. Snell (1952): “Applications of martingale system theorems,” Trans. Am. Math. Soc. 73, pp. 293–312.
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© 1977 Springer-Verlag, New York Inc.
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Lamperti, J. (1977). Martingale Theory. In: Stochastic Processes. Applied Mathematical Sciences, vol 23. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9358-0_10
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DOI: https://doi.org/10.1007/978-1-4684-9358-0_10
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