Stochastic Differential Equations

Stochastic differential equations provide a powerful mathematical framework for the continuous time modeling of asset prices and general financial markets. We consider both scalar and vector stochastic differential equations which allow us to model feedback effects in the market. Explicit solutions will be given in certain cases. Furthermore, questions related to the existence and uniqueness of solutions will be discussed. We also mention stochastic differential equations with jumps which allow us to model event driven uncertainty.