Delayed Gambler's Ruin
  We present here a new extended model of the gambler's ruin problem by incorporating delays in receiving of rewards and paying of penalties. When there is a difference between two delays, an exact analysis of the ruin probability is difficult. We derive an approximate scheme to find an effective shift in the initial assets of the gambler. Through comparison against computer simulations, this approximation is shown to work for small differences between the two delays. 
Tomohisa Imai and Toru Ohira
physics.soc-ph math.PR