On Maximal Inequalities for some Jump Processes
AbstractWe present a solution to the considered in  and  optimal stopping problem for some jump processes. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the normal reflection and smooth fit may break down and the latter then be replaced by the continuous fit. The derived result is applied for determining the best constants in maximal inequalities for a compound Poisson process with linear drift and exponential jumps.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-060.
Length: 16 pages
Date of creation: Sep 2006
Date of revision:
Jump process; stochastic differential equation; maximum process; optimal stopping problem; compound Poisson process; Ito’s formula; integro-differential free-boundary problem; normal reflection; continuous and smooth fit; maximality principle; maximal inequalities;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- 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.
- Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
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