Optimal Strategies Of The Perpetual Executive Stock Options With The Dilution Effect

Executive stock options (ESOs) plays an increasingly important role in modern corporate governance, so how to make a reasonable pricing for ESOs has become an important issue facing enterprises. In the paper,we mainly discuss a problem that the dilution effect, which caused by exercise the ESOs, influence on the optimal strategies and pricing for the perpetual ESOs with unrestricted exercise.First of all,by use of the executive’s utility maximization and follow Rogers and Scheinkman [4] (2007) method, we have established a stochastic optimal control model for the executive stock options with finite-horizon under considering the dilution effect and obtained the definite problem of the corresponding parabolic variational inequality ,then given their financial significance.Secondly, we give the expression of the solution of the above parabolic variational inequalities and initial value problem of ordinary differential equation with free bound-ary satisfied under the risk-free interest rate r = 0.Finally introduce some properties of the solution and the free boundary.Finally, we give the expression of the optimal implementation strategies.In the risk-free interest rate r = 0 and exponential utility function, we strictly prove the veri-fication theorem:the solution of the variational inequality problem is the value function of the stochastic optimal control problems. And then we discuss the nature and unique-ness of the optimal implementation strategy.