Stochastic approximation algorithms for trailing stop

Trailing stops are often used in stock trading to limit a maximum-possible loss and to lock in a profit. In this venue, it is important to identify the optimal trailing stop percentage, which is difficult to find and no apparent analytic technique can be applied directly. This work develops stochastic approximation algorithms to estimate the optimal trailing stop percentage. A modification using projection is also proposed to ensure the approximation sequence constructed to stay in a bounded region. Convergence of the algorithm is obtained. Moreover, interval estimates are constructed. Simulation examples are presented to compare our algorithm with Monte Carlo methods. Finally, real market data are used to demonstrate the algorithms.