MATH 3589 Lecture Notes - Lecture 2: Random Variable, Risk Neutral, Sample Space

• School: Ohio State University
• Department: Mathematics
• Course: MATH 3589
• Professor: John Holmes

Document Summary

Let p be the actual prob- measures are positive for every sequence of coin tosses . Let z( ) be the radon- ability measure and ep be the risk-neutral probability measure, and assume both. Nikod yn derivative of ep with respect to p, and let zn, n = 0, 1, . For 0 n m n , xed but arbitrary integers, let y be a random variable depending only upon the rst m coin tosses. Then the time t = n expected value of y under the risk-neutral probability measure is the sum over all future coin toss sequences = n+1 . Y ( )ep( ). (here, y ( ) = y ( 1 . M) is the value of the random variable y evaluated at 1 . Multiplying by a complicated 1, we nd een[y ] = x = n+1 m. P( ) where we are using the notation p( ) = p( 1 .