I'm trying to work on this problem:
I have a biased random walk. With probability $0.7$, you gain $1$ and with probability $0.3$, you lose $1$. You start at $0$.
Set a stop loss at $-10$. Once the random walk hits $-10$ it terminates and uses -10 as the final value. Walk 100 steps, what is the expectation?
If this were a simple random walk, I can have a probability distribution function for the first passage time $\tau_{-10}$. However, this is a biased random walk. I'm not sure how I can proceed.
Can I get some help? Thank you.