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 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

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.

Mean-field controllability and decentralized stabilization of Markov chains

2017 ◽  
Author(s):  
Karthik Elamvazhuthi ◽  
Matthias Kawski ◽  
Shiba Biswal ◽  
Vaibhav Deshmukh ◽  
Spring Berman
Keyword(s):  
Markov Chains ◽  
Mean Field ◽  
Decentralized Stabilization
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