2 citations · 6 across the 13 of their papers we have counts for
18 papers
Target-Generated Dirichlet Problems in State-Constrained Stochastic Control
Erhan Bayraktar, Haichuan Ding, Ibrahim Ekren
We study state-constrained stochastic control problems with a scalar surplus . Controls for which the drift and volatility of vanish at zero define a lower-dimensiona…
A one-sided constrained martingale transport between two uniform laws
Erhan Bayraktar, Xin Zhang
We minimize over martingale couplings of and satisfying , where has convex derivative. Fea…
Prediction with Five Experts and Geometric Stopping: A Probabilistic Construction and Analytic Verification
Erhan Bayraktar, Ibrahim Ekren, Nikolaos Kolliopoulos
We present a solution of the limiting five-expert prediction problem with geometric stopping, based on stochastic calculus and partial differential equations. If is the stoppin…
Mean-field optimal stopping with endogenous quantile cutoffs
Erhan Bayraktar, Ibrahim Ekren, Xihao He
We study a mean-field optimal stopping problem with an endogenous population-level shutdown. All remaining agents stop when the survival mass falls below a prescribed threshold. We…
Kullback-Leibler Mirror-Prox for Measure-Valued Variational Inequalities and Mean-Field Equilibria
Erhan Bayraktar, Ibrahim Ekren, Lu Vy +1
We study the computation of static mean-field equilibria on a compact state space by formulating the equilibrium condition as a variational inequality over probability measures. We…
Quantitative Particle Approximation for Controlled Nonlinear Filtering
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
We estimate convergence rates of value functions for particle approximations of a controlled nonlinear filtering problem. The state is a McKean--Vlasov diffusion on the flat torus,…
A comparison principle for Wasserstein PDEs with state- and law-dependent common noise
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
We prove a comparison principle for a class of second-order Hamilton--Jacobi--Bellman equations on the Wasserstein space whose second-order term is generated by a general common-no…
Uniform-in-time propagation of chaos for consensus-based minimax algorithm
Erhan Bayraktar, Zhiyan Ding, Ibrahim Ekren +1
We study the large-population convergence of a consensus-based algorithm for the saddle point problem proposed by ArXiv: 2212.12334, establishing the uniform-in-time propagation of…
Viscosity and minimax solutions for path-dependent Hamilton-Jacobi equations in infinite dimensions and related differential games
Erhan Bayraktar, Mikhail Gomoyunov, Christian Keller
We establish new results for path-dependent Hamilton-Jacobi equations with nonlinear monotone, and coercive operators on Hilbert space, which were initially studied in Bayraktar an…
Contracting a crowd of heterogeneous agents
Guillermo Alonso Alvarez, Erhan Bayraktar, Ibrahim Ekren
We study optimal contract design for large populations of heterogeneous agents whose actions generate network spillovers represented by an interaction function. In a linear-quadrat…
Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space
Erhan Bayraktar, Ibrahim Ekren, Xihao He +1
In this paper, we prove a comparison result for semi-continuous viscosity solutions of a class of second-order PDEs in the Wasserstein space. This allows us to remove the Lipschitz…
Uniform-in-time weak propagation of chaos for consensus-based optimization
Erhan Bayraktar, Ibrahim Ekren, Hongyi Zhou
We study the uniform-in-time weak propagation of chaos for the consensus-based optimization (CBO) method on a bounded searching domain. We apply the methodology for studying long-t…
Viscosity Solutions of Fully second-order HJB Equations in the Wasserstein Space
Erhan Bayraktar, Hang Cheung, Ibrahim Ekren +3
In this paper, we show that the value functions of mean field control problems with common noise are the unique viscosity solutions to fully second-order Hamilton-Jacobi-Bellman eq…
Sequential optimal contracting in continuous time
Guillermo Alonso Alvarez, Erhan Bayraktar, Ibrahim Ekren +1
In this paper we study a principal-agent problem in continuous time with multiple lump-sum payments (contracts) paid at different deterministic times. We reduce the non-zero sum St…
Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
In this paper, we provide a convergence rate for particle approximations of a class of second-order PDEs on Wasserstein space. We show that, up to some error term, the infinite-dim…
Non-parametric estimates for graphon mean-field particle systems
Erhan Bayraktar, Hongyi Zhou
We consider the graphon mean-field system introduced in the work of Bayraktar, Chakraborty, and Wu. It is the large-population limit of a heterogeneously interacting diffusive part…
Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions th…
A PDE approach for regret bounds under partial monitoring
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Was…