Classic ruin theory assumes that the income is constant and that only the losses are random with an underlying distribution.
Suppose we want to determine the risk of ruin for a game (for example poker), where also the winnings are random.
Let $\psi(u)$ denote the risk of ruin, starting from initial surplus $u$. We assume that the winnings/losses in each game follow a normal distribution with mean $\mu>0$. The game is played until the player is broke or his surplus goes to infinity.
Classical ruin theory doesn't seem to apply because of the non-constant income. I am grateful for any advice on how to approach this problem.