In the classical Kalman-Bucy filter and in the subsequent literature so far, it has been assumed that the initial value of the signal process is independent of both the noise of the signal and of the noise of the observations.The purpose of this paper is to prove a filtering equation for a...

We study a membrane voltage potential model by means of stochastic control of meanfield stochastic differential equations (SDEs) and by deep learning techniques. The mean-field stochastic control problem is a new type, involving the expected value of a combination of the state X(t) and the...

We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal option price, and the corresponding equivalent martingale...