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math.PR2008
On the expected diameter of an L2-bounded martingale
Lester E. Dubins, David Gilat, Isaac Meilijson
It is shown that the ratio between the expected diameter of an L2-bounded martingale and the standard deviation of its last term cannot exceed sqrt(3). Moreover, a one-parameter fa…
math.PR2008
On the adjustment coefficient, drawdowns and Lundberg-type bounds for random walk
Isaac Meilijson
Consider a random walk whose (light-tailed) increments have positive mean. Lower and upper bounds are provided for the expected maximal value of the random walk until it experience…