Nonlinear and Stochastic Dynamical Systems Modeling Price Dynamics

Abstract

In many economic and financial processes mathematical modeling leads to nonlinear and stochastic dynamical systems. The interplay of stochastic and nonlinear effects is important under many aspects. Whereas the dynamic behavior of deterministic dynamical system may be characterized by the attractors of its trajectories, stochastic “perturbations” will lead to a even more complex behavior e.g. to transitions, even to jumps between attractors like equilibria. This thesis has as main aims: analyzing the effects of nonlinearities and stochasticity on price dynamics of assets, in general, modeling the price dynamics of oil, as a special commodity and determining option prices and optimal hedging strategies for commodities like oil.