On Martingales and the Use of Optional Stopping Theorem to Determine the Mean and Variance of a Stopping Time
Applied and Computational Mathematics
Volume 3, Issue 6-1, December 2014, Pages: 12-17
Received: Aug. 1, 2014;
Accepted: Aug. 6, 2014;
Published: Sep. 5, 2014
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Ganiyu, A. A., Department of Mathematics, Adeyemi College of Education, Ondo, Nigeria
Fakunle, I., Department of Mathematics, Adeyemi College of Education, Ondo, Nigeria
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This paper examines the roles martingale property played in the use of optional stopping theorem (OST). It also examines the implication of this property in the use of optional stopping theorem for the determination of mean and variance of a stopping time. A simple example relating to betting system of a gambler with limited amount of money has been provided. The analysis of the betting system showed that the gambler leaves with the same amount of money as when he started and therefore satisfied martingale property. Linearity of expectation property was used as a reliable tool in the use of the martingale property.
Martingales, Gambler, Random Walk, Stopping Time, Optional Stopping Theorem, Mean, Variance
To cite this article
Ganiyu, A. A.,
On Martingales and the Use of Optional Stopping Theorem to Determine the Mean and Variance of a Stopping Time, Applied and Computational Mathematics. Special Issue: Computational Finance.
Vol. 3, No. 6-1,
2014, pp. 12-17.
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[10 ] Ugbebor O.O., Ganiyu A.A. and Fakunle I. (2012). “Optional Stopping Theorem as an Indispensable Tool in the Determination of Ruin Probability and Expected Duration of a Game”. Journal of the Nigerian Association of Mathematical Physics”, Vol. 21, Pp 85-93.