A direct solution method for pricing options involving the maximum process. (English) Zbl 1391.91155
The authors provide explicit solutions for optimal stopping problems related to a diffusion process and its running maximum. They use excursion theory for Markov processes and reformulate the original two-dimensional problem as an infinite number of one-dimensional ones. The solution method does not suppose the existence of an optimal threshold and does not impose a smooth-fit condition. The authors illustrate the method through classical and new examples.
Reviewer: Pavel Stoynov (Sofia)
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 60J60 | Diffusion processes |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
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