We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. prove that the solution to MFG can be characterized in terms forward-backward stochastic differential equation (FBSDE) with possibly singular terminal condition on backward component or, equivalently, an FBSDE finite value yet driver. Extending method continuation linear-quadratic FBSDEs driver, w...

Abstract Pairs trading is a typical example of convergence strategy. Investors buy relatively under-priced assets simultaneously, and sell over-priced to exploit temporary mispricing. This study examines optimal pairs strategies under symmetric non-symmetric constraints. Under the assumption that price spread pair correlated securities follows mean-reverting Ornstein-Uhlenbeck(OU) process, anal...

We propose a mean-field optimal control problem for the parameter identification of given pattern. The cost functional is based on Wasserstein distance between probability measures modeled and desired patterns. first-order optimality conditions corresponding to are derived using Lagrangian approach level. Based these we gradient descent method identify relevant parameters such as angle rotation...

Consider the optimal control of a manufacturing system consisting of stages in which a single consumable good is produced in a random jump environment. At each stage of the manufacturing process there are workstations that can fail and be repaired. The workstations are assumed to have different operating parameters for a given stage. The mean time to failure for a given workstation, on a given ...

We consider observations of a random process (or a random field), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. Optimality criteria for parameter estimation are to be based here on the mean square errors (MSE) of estimators. We mention briefly expressions obtained for very small samples via probability densities of estimat...

We study linear estimators for the weighted integral of a stochastic process. The process may only be observed on a nite sampling design. The error is deened in mean square sense, and the process is assumed to satisfy Sacks-Ylvisaker regularity conditions of order r 2 N 0. We show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators. Hereby we ...