Let St be the price of stock at time t and suppose that at t

Let S_t be the price of stock at time t and suppose that at times of a Poisson process with rate ? the price is multiplied by a random variable X_i > 0 with mean µ and variance ?².

Let S_t be the price of stock at time t and suppose that at times of a Poisson process with rate lambda the price is multiplied by a random variable X_i > 0 with mean mu and variance sigma^2. That is, S_t = S_0 Pi I = 1 N(t) X_i, where the product is 1 if N(t) = 0. Find ES(t) and var S(t).

Solution