38 citations · 150 across the 39 of their papers we have counts for
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Strong solutions of stochastic equations with rank-based coefficients
Tomoyuki Ichiba, Ioannis Karatzas, Mykhaylo Shkolnikov
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by it…
On the one-sided Tanaka equation with drift
Ioannis Karatzas, Albert N. Shiryaev, Mykhaylo Shkolnikov
We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift λ. We observe a dichotomy in terms of the values of…
Convergence rates for rank-based models with applications to portfolio theory
Tomoyuki Ichiba, Soumik Pal, Mykhaylo Shkolnikov
We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Convergence rate for the total variation metri…
Large volatility-stabilized markets
Mykhaylo Shkolnikov
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of d…