Financial Mathematics

Chapter 8

General Multi-Asset Multi-Period Model

In this chapter we construct a general multi-asset discrete-time model with a finite state space. Most of the results of Chapter 5 and 7 will be generalized so that a single-period model and a binomial tree model become special cases of a more general framework.

8.1 Main Elements of the Model

Let us describe all main components of a general multi-period model defined on a filtered probability space $\left(\Omega ,ℱ,\mathbb{P},\mathbb{F}\right)$.

• There are T + 1 trading dates, t ∊{0, 1, 2,...,T}. Denote the collection of trading dates by T.
• A state space Ω = {ω1,ω2,...,ωM} represents all possible final states (or scenarios) of the world at time T.

• A filtration $\mathbb{F}={\left\{{ℱ}_t\right\}}_{t\in T}$ describes the arrival of information about the market with the ...