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Optimization of joint $p$-variations of Brownian semimartingales


 
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1. Title Title of document Optimization of joint $p$-variations of Brownian semimartingales
 
2. Creator Author's name, affiliation, country Emmanuel Gobet; École Polytechnique; France
 
2. Creator Author's name, affiliation, country Nicolas Landon; École Polytechnique; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) $p$-variation; almost-sure convergence; optimal stopping times
 
3. Subject Subject classification 60F15; 60G17; 60G40
 
4. Description Abstract We study the optimization of the joint $(p^Y,p^Z)$-variations of two continuous semimartingales $(Y,Z)$ driven by the same Itô process $X$. The $p$-variations are defined on random grids made of finitely many stopping times. We establish an explicit asymptotic lower bound for our criterion, valid in rather great generality on the grids, and we exhibit minimizing sequences of hitting time form. The asymptotics is such that the spatial increments of $X$ and the number of grid points are suitably converging to 0 and $+\infty$ respectively.
 
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7. Date (YYYY-MM-DD) 2014-06-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2975
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-2975
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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