Modeling a financial market
Mathematical Finance : Asset Pricing

The natural framework is to consider a probabilized space in order to take into account the hazards and uncertainty observed on financial markets. We therefore consider a $\mathrm{\Omega }\ne Ø$ whose elements ω are the possible future market states between t = 0 (today) and a future horizon, say a date T > 0. It is clearly impossible to simply describe a state $\omega \in \mathrm{\Omega }$ future of the market. Such a state represents everything that will happen between t = 0 and t = T. Even after time has elapsed, we will have observed prices executed, and quantities too, but other features of the market are not necessarily...