Imperial College London
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ProfessorDamianoBrigo

Faculty of Natural Sciences, Department of Mathematics

Chair in Mathematical Finance
 
 
 
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damiano.brigo CV

 
 
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Location

 

805Weeks BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Brigo:2020:10.1016/j.spa.2019.11.003,
author = {Brigo, D and Jeanblanc, M and Vrins, F},
doi = {10.1016/j.spa.2019.11.003},
journal = {Stochastic Processes and their Applications},
pages = {3895--3919},
title = {SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions},
url = {http://dx.doi.org/10.1016/j.spa.2019.11.003},
volume = {130},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Peacocks are increasing processes for the convex order. To any peacock, one can associate martingales with the same marginal laws. We are interested in finding the diffusion associated to the uniform peacock, i.e., the peacock with uniform law at all times on a time-varying support . Following an idea from Dupire (1994), Madan and Yor (2002) propose a construction to find a diffusion martingale associated to a Peacock, under the assumption of existence of a solution to a particular stochastic differential equation (SDE). In this paper we study the SDE associated to the uniform Peacock and give sufficient conditions on the (conic) boundary to have a unique strong or weak solution and analyse the local time at the boundary. Eventually, we focus on the constant support case. Given that the only uniform martingale with time-independent support seems to be a constant, we consider more general (mean-reverting) diffusions. We prove existence of a solution to the related SDE and derive the moments of transition densities. Limit-laws and ergodic results show that the transition law tends to a uniform distribution.
AU  - Brigo,D
AU  - Jeanblanc,M
AU  - Vrins,F
DO  - 10.1016/j.spa.2019.11.003
EP  - 3919
PY  - 2020///
SN  - 0304-4149
SP  - 3895
TI  - SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions
T2  - Stochastic Processes and their Applications
UR  - http://dx.doi.org/10.1016/j.spa.2019.11.003
UR  - http://hdl.handle.net/10044/1/75153
VL  - 130
ER  -
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