Perpetual options and Canadization through fluctuation theory. (English) Zbl 1039.60044

Summary: It is shown that one is able to evaluate the price of perpetual calls, puts, Russian and integral options directly as the Laplace transform of a stopping time of an appropriate diffusion using standard fluctuation theory. This approach is offered in contrast to the approach of optimal stopping through free boundary problems. Following ideas of P. Carr [Rev. Fin. Studies 11, 597–626 (1998)], we discuss the Canadization of these options as a method of approximation to their finite time counterparts. Fluctuation theory is again used in this case.


60G40 Stopping times; optimal stopping problems; gambling theory
60J65 Brownian motion
91B26 Auctions, bargaining, bidding and selling, and other market models
91B28 Finance etc. (MSC2000)
91B70 Stochastic models in economics
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