Discounted Optimal Stopping for Maxima of some Jump-Diffusion Processes
We present solutions to some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems where the normal reflection and smooth fit may break down and the latter then be replaced by the continuous fit. The results can be interpreted as pricing perpetual American lookback options with fixed and floating strikes in a jump-diffusion model.
|Date of creation:||Sep 2006|
|Date of revision:|
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- Gapeev Pavel V. & Kühn Christoph, 2005. "Perpetual convertible bonds in jump-diffusion models," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 15-31, January.
- S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
- Duistermaat, J.J. & Kyprianou, A.E. & van Schaik, K., 2005. "Finite expiry Russian options," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 609-638, April.
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