An optimal stopping problem on the finite-step simple random walk with absorbent boundaries

This paper proposes a model of finite-step simple random walk with absorbent boundaries. We address a problem of optimal stop for this model, which is defined as the absorbent boundary value with maximum profit. Compared with many existing optimal stopping investigations in the random process, the optimal stopping time is given based on the classical probability computation within finite steps which is more easier to comprehend. The result obtained in this paper may provide some useful guidelines for real applications associated with the finite-step simple random walk such as stock market and gambling game.