Alongside the British put option (Peskir and Samee [<italic>Appl. Math. Finance</italic>, 2011, <bold>18</bold>, 537--563]) we present a new call option where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff...

Motivated by applications in option pricing theory (Peskir, 1997b), (Research Report No. 386, Dept. Theoret. Statist. Aarhus, 19 pp.) we formulate and solve the following problem. Given a standard Brownian motion B=(Bt)t[greater-or-equal, slanted]0 and a centered probability measure [mu] on...

We show that in the absence of any information about the ‘hidden’ target in terms of the observed sample path, and irrespectively of the distribution law of the observed process, the ‘median’ rule is optimal in both the space domain and the time domain. While the fact that the median...

We show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal...

We present a new put option where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in...