Derivatives and Stochastic Control: Passport Options
Most options we have seen so far give the holder a choice at one specific moment. With a European option, you decide at expiry. With an American option, you pick the best time to exercise. But what if the option let you actively trade during its entire life, and then insured you against losses? That is the idea behind the passport option, and Chapter 27 of Wilmott’s book uses it to introduce stochastic control.