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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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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 (Ω,,,F).

  • There are T + 1 trading dates, t ∊{0, 1, 2,...,T}. Denote the collection of trading dates by T.
  • A state space Ω = {ω12,...,ωM} represents all possible final states (or scenarios) of the world at time T.
  • A filtration F={t}tT describes the arrival of information about the market with the ...

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