scholarly journals A NOTE ON A QUESTION RELATED TO KOLMOGOROV FORWARD EQUATION

2014 ◽  
Vol 27 (1) ◽  
pp. 35-37
Author(s):  
Joongul Lee
Keyword(s):  
Forward Equation ◽  
Kolmogorov Forward Equation

scholarly journals Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes

2018 ◽  
Vol 5 (1) ◽  
pp. 1556192 ◽  
Author(s):  
Mario A. Natiello ◽  
Raúl H. Barriga ◽  
Marcelo Otero ◽  
Hernán G. Solari ◽  
Yuriy Rogovchenko
Keyword(s):  
Forward Equation ◽  
Kolmogorov Forward Equation ◽  
Population Processes

Controllability and decentralized stabilization of the Kolmogorov forward equation for Markov chains

Automatica ◽  
2021 ◽  
Vol 124 ◽  
pp. 109351
Author(s):  
Karthik Elamvazhuthi ◽  
Shiba Biswal ◽  
Spring Berman
Keyword(s):  
Markov Chains ◽  
Decentralized Stabilization ◽  
Forward Equation ◽  
Kolmogorov Forward Equation

scholarly journals From Bachelier to Dupire via optimal transport

2021 ◽  
Vol 26 (1) ◽  
pp. 59-84
Author(s):  
Mathias Beiglböck ◽  
Gudmund Pammer ◽  
Walter Schachermayer
Keyword(s):  
Optimal Transport ◽  
Formal Solution ◽  
Mathematical Finance ◽  
Forward Equation ◽  
Survey Article ◽  
Formal Derivation ◽  
Kolmogorov Forward Equation ◽  
Free Model ◽  
Volatility Surface ◽  
Phd Thesis

AbstractFamously, mathematical finance was started by Bachelier in his 1900 PhD thesis where – among many other achievements – he also provided a formal derivation of the Kolmogorov forward equation. This also forms the basis for Dupire’s (again formal) solution to the problem of finding an arbitrage-free model calibrated to a given volatility surface. The latter result has rigorous counterparts in the theorems of Kellerer and Lowther. In this survey article, we revisit these hallmarks of stochastic finance, highlighting the role played by some optimal transport results in this context.

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

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