ABSTRACT
This section is devoted to the rigorous study of the Black-Scholes model of a (B,S)-market with time horizon T < ∞.
Let (Ω,F ,F, P ) be a stochastic basis. Here, filtration F = (Ft)t≤T represents a continuous information flow that is parameterized by a time parameter t ∈ [0, T ] in contrast to the discrete time case of the previous chapter. It is natural to assume that Ft (being the information up to time t) is a σ-algebra, that is,
1. ∅, Ω ∈ Ft; 2. A ∈ Ft ⇒ Ω \A ∈ Ft (closed under taking complements); 3. (Ak)∞k=1 ⊂ Ft ⇒ ∪∞k=1Ak ∈ Ft (closed under taking countable unions); 4. (Ak)∞k=1 ⊂ Ft ⇒ ∩∞k=1Ak ∈ Ft (closed under taking countable intersec-
tions).
