Statistical Physics Approach to the Optimal Transport Problem

Higher Order Statistical Approach to Nonlinear Stochastic Optimal Control Problem

This paper presents the formulation of an optimal control methodology for nonlinear stochastic systems, where the control objective is to obtain a feedback law that would minimizes the higher order statistics associated with the traditional integral quadratic cost. The two part control scheme proposed here consist of approximating the probability density function associated with the nonlinear p...

Statistical Physics Approach to M - theory Integrals ∗

We explain the concepts of computational statistical physics which have proven very helpful in the study of Yang-Mills integrals, an ubiquitous new class of matrix models. Issues treated are: Absolute convergence versus Monte Carlo computability of near-singular integrals, singularity detection by Markov-chain methods, applications to asymptotic eigenvalue distributions and to numerical evaluat...

a benchmarking approach to optimal asset allocation for insurers and pension funds

uncertainty in the financial market will be driven by underlying brownian motions, while the assets are assumed to be general stochastic processes adapted to the filtration of the brownian motions. the goal of this study is to calculate the accumulated wealth in order to optimize the expected terminal value using a suitable utility function. this thesis introduced the lim-wong’s benchmark fun...

The optimal partial transport problem

Given two densities f and g, we consider the problem of transporting a fraction m ∈ [0, min{‖f‖L1 , ‖g‖L1}] of the mass of f onto g minimizing a transportation cost. If the cost per unit of mass is given by |x − y|2, we will see that uniqueness of solutions holds for m ∈ [‖f ∧ g‖L1 , min{‖f‖L1 , ‖g‖L1}]. This extends the result of Caffarelli and McCann in [8], where the authors consider two den...

An Approach to the Sediment Transport Problem