1) 100 ants are uniformly placed on a [0,1] line, and they randomly travel toward either 0 or 1. When one collides with the other, they exchange directions. Assuming that each ant travels at the speed of 1 per hour, how long would it take for the last ant to reach the either end? 2) What is E(exp(Wt)), E((Wt)^4),... where Wt is a standard Brownian? 3) What is a martingale? Is E(Wt^2-t) a martingale? why? 4) How would you simulate a covariance matrix of 1,000 stocks where each pair has nonzero correlation? 5) Write down a black-scholes equations. What is delta, and how does it change when it approaches the maturity?
