Local times of ranked continuous semimartingales

By Adrian Banner, R. Ghomrasni. 2008

70 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/461f796b6f0b02fc221a03410fc54de282e823a7

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In Finance

In Management Science and Operations Research

Citations in the corpus

HYBRID ATLAS MODELS (2009, methodology): “Instead of taking Dyson’s process or the spin glass theory as our model for rankings in equity markets, we obtain the ranked particle system through a general formula of Banner & Ghomrasni [4] for continuous semimartingales in the hybrid Atlas model.”
Systems of Brownian particles with asymmetric collisions (2012, methodology): “Then with the notation Nk(t) for the set of indices of particles at the location of the kth ranked particle at time t , the Banner and Ghomrasni [3] formula dRXk (t) = n∑ i=1 1{rX(t)(Xi(t))=k} dXi(t) + 1 |Nk(t)| ( n∑ =k+1 dΛ(k, )(t) − k−1∑ =1 dΛ( ,k)(t) ) (1.7) (cf. Theorem 2.3 in [3]) shows that th”
Stochastic Portfolio Theory: an Overview (2009, methodology): “A derivation of this result, under appropriate conditions that we choose not to broach here, can be found on pp. 76-79 of Fernholz (2002); see also Banner & Ghomrasni (2007) for generalizations.”
Convergence rates for rank-based models with applications to portfolio theory (2011, background): “Among the more recent ones, see Banner, Fernholz and Karatzas [4], Banner and Ghomrasni [5], McKean and Shepp [30], Pal and Pitman [32], Jourdain and Malrieu [25], Chatterjee and Pal [11, 12], Ichiba and Karatzas [23], Ichiba et al. [24], Pal and Shkolnikov [33], and Shkolnikov [40, 41].”
Strong solutions of stochastic equations with rank-based coefficients (2011, background): “Again, either there is a triple collision at τ [2] and the proof is complete, or else we go ahead with the construction to extend the solution up to a time τ [3].”