We study state-constrained stochastic control problems with a scalar surplus $R \geq 0$. Controls for which the drift and volatility of $R$ vanish at zero define a lower-dimensional Hamilton-Jacobi-Bellman equation. Starting from control-wise state-constraint viscosity inequalities, we prove that the upper and lower li...
Erhan Bayraktar, Hai-Chuan Ding, Ibrahim Ekren· 0 citations
We present a solution of the limiting five-expert prediction problem with geometric stopping, based on stochastic calculus and partial differential equations. If $\delta$ is the stopping probability, the minimax expected regret from tied initial scores is $45\pi^2/(512\sqrt{2\delta})+o(\delta^{-1/2})$ as $\delta\downar...
Erhan Bayraktar, Ibrahim Ekren, N. Kolliopoulos· 3 citations
It is shown that the alternating COMB control attains the limiting Hamiltonian maximum exactly when the two highest scores coincide and the third- and fourth-highest scores coincide, and that the alternating COMB control attains the limiting Hamiltonian maximum exactly when the two highest scores coincide.
Erhan Bayraktar, Ibrahim Ekren, N. Kolliopoulos· 2 citations
This work estimates convergence rates of value functions for particle approximations of a controlled nonlinear filtering problem and establishes uniform value-function error bounds of order under smoothness of the data, uniform ellipticity, and regularity of this Hamiltonian.
Erhan Bayraktar, Ibrahim Ekren, Xi-Hao He et al.· 0 citations
An entropic variant of Korpelevich's extragradient algorithm---the Kullback--Leibler Mirror-Prox method---in which Euclidean projections are replaced by relative-entropy proximal steps, and a KL-type Tikhonov regularization that selects the equilibrium minimizing relative entropy with respect to a reference measure is...
Erhan Bayraktar, Ibrahim Ekren, Lukianiuk Vy et al.· 0 citations
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