Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets
Maraia, Ramona (2016)
Diplomityö
Maraia, Ramona
2016
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe201603308917
https://urn.fi/URN:NBN:fi-fe201603308917
Tiivistelmä
The aim of this study is to propose a stochastic model for commodity markets linked
with the Burgers equation from fluid dynamics. We construct a stochastic particles
method for commodity markets, in which particles represent market participants. A
discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation
and the connection of this model with stochastic differential equations are also studied.
Further, based on the law of large numbers, we prove the convergence, for large N, of
a system of stochastic differential equations describing the evolution of the prices of
N traders to a deterministic partial differential equation of Burgers type. Numerical
experiments highlight the success of the new proposal in modeling some commodity
markets, and this is confirmed by the ability of the model to reproduce price spikes
when their effects occur in a sufficiently long period of time.
with the Burgers equation from fluid dynamics. We construct a stochastic particles
method for commodity markets, in which particles represent market participants. A
discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation
and the connection of this model with stochastic differential equations are also studied.
Further, based on the law of large numbers, we prove the convergence, for large N, of
a system of stochastic differential equations describing the evolution of the prices of
N traders to a deterministic partial differential equation of Burgers type. Numerical
experiments highlight the success of the new proposal in modeling some commodity
markets, and this is confirmed by the ability of the model to reproduce price spikes
when their effects occur in a sufficiently long period of time.