A class of remarkable submartingales
By Ashkan Nikeghbali. 2005
52 citations recorded by the source corpus.
In this paper, we consider the special class of positive local submartingales (Xt) of the form Xt=Nt+At, where the measure is carried by the set {t:Xt=0}. We show that many examples of stochastic processes studied in the literature are in this class and propose a unified approach based on martingale techniques for studying them. In particular, we establish some martingale characterizations for these processes and compute explicitly some distributions involving the pair (Xt,At). We also associate with X a solution to the Skorokhod's stopping problem for probability measures on the positive half-line.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/23ab03fcdea73fa6c7e6da066e4e8bdd3fc9de25
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In Finance
- Ashkan Nikeghbali
- Hongzhong Zhang
- Olympia Hadjiliadis
- Marc Yor
- Vadim Linetsky
- Daniel Dufresne
- Hiroyuki Matsumoto
- Pierre Patie
In Management Science and Operations Research
Citations in the corpus
- An essay on the general theory of stochastic processes (2005, methodology): “6 and to the Skorokhod’s stopping problem, see [61].”
- Drawdowns and the Speed of Market Crash (2012, background): “Our results extend the work of Taylor (1975), Lehoczky (1977) and Nikeghbali (2006) from which it is possible to extract the Laplace transform of the random variable Xρ under drifted Brownian motion dynamics and general diffusion dynamics.”
- Doob's maximal identity, multiplicative decompositions and enlargements of filtrations (2005, background): “Remark 2.13. Similar formulas are derived in [ 18 ] from different considerations.”