Perpetual American Standard and Lookback Options with Event Risk and Asymmetric Information

We derive closed-form solutions to the perpetual American standard and floating-strike lookback put call options in an extension of Black--Merton--Scholes model with event risk asymmetric information. It is assumed that contracts are terminated by their writers linear or fractional recoveries at last hitting times for underlying asset price process its ultimate maximum minimum over infinite time interval which not stopping respect reference filtration. show optimal exercise holders first reaches some lower upper stochastic boundaries depending on current values running minimum. The proof based reduction original problems associated free-boundary solution latter means smooth-fit normal-reflection conditions. proven be maximal minimal first-order nonlinear ordinary differential equations.