A Variational Inequality Sufficient Condition for Optimal Stopping with Application to an Optimal Stock Selling Problem

We give a variational inequality sufficient condition for optimal stopping problems. This result is illustrated by computing solutions to an optimal stock selling problem. The stock selling problem has a model for the stock price which initially has a “hot” growth rate and then “tanks”. Solution of the conditions allow computation of both the value function and the optimal stopping times. The implications on the investors behavior of different parameter settings for different utility functions are discussed.