Using Stochastic Approximation Algorithms in Stock Liquidation

AbstractFor hybrid geometric Brownian motion stock liquidation models, it has been proved that the optimal selling policy is of threshold type, which can be obtained by solving a set of two-point boundary value problems. The total number of equations to be solved is the same as that of the numbers of states of the underlying Markov chain. To reduce the computational burden, this work develops Monte Carlo algorithms, which are recursive and are stochastic optimization type, to approximate the optimal threshold values in stock trading. Then asymptotic properties of the proposed algorithms such as the convergence and rates of convergence are developed.