1 Introduction
-
a is the number of ESOs held by the manager at time 0 before exercise, \(0< a \leq M\);
-
\(m_{t}\) is the number of ESOs exercised by the manager until time t;
-
\(S_{t}\) is the stock price at time t, and s is the stock price at time 0, \(0< s<+\infty\);
-
K is the strike price of ESOs, and r is the risk-free rate, where r is a constant and \(r>0\);
-
x is the manager’s wealth at time 0 before exercise, \(0\leq x<+\infty\);
-
\(U(\cdot)\) is the utility function of the manager, which is concave and increasing.