Problem 4
Suppose {Wideo is a standard Browly motion. Le {M}cy be the maximum
Mi-max W.
-
For a fixed 8 >0 and N > Owe define the random variable
7 (8) - N Amint 2 0:W, S M.-)
It is equal to the first time the drawdown reaches the valued, if it happens before
time N. or to N otherwise
(a) Prove thin the random variable T() is a stopping time,
(b) Calculate the expected value of W
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