Problem bank

Problem 300 of 333MediumStochastic ProcessesP300

A stock that doubles or halves

  1. A stock trades at 100. Each day it doubles with probability 1/31/3 or halves with probability 2/32/3, independently of the past. You watch it until it first reaches 400 or 25.

    What is the probability that it reaches 400 first? How many days does the wait last on average?