Assume the risk-free asset Bt and the (non-dividend paying) stock St follow the dynamics of the Black-Scholes model (with interest rate r>0, stock drift R and volatility >0 ). Consider the perpetual American option with payoff 2((KSr)+)3 where is the exercise time. Assume that the smooth pasting condition holds. Write the corresponding free boundary problem and find the price of the option. Assume the risk-free asset Bt and the (non-dividend paying) stock St follow the dynamics of the Black-Scholes model (with interest rate r>0, stock drift R and volatility >0 ). Consider the perpetual American option with payoff 2((KSr)+)3 where is the exercise time. Assume that the smooth pasting condition holds. Write the corresponding free boundary problem and find the price of the option