Dynamic Hedging with Stochastic Differential Utility

Let (Ω, =,P) denote a probability space, Ξ a locally compact metric spacewith a countable basis E, aσ-field of Borelians in Ξ, I an interval of the realline, and for each t ∈ I, X t is a stochastic process such that X t :(Ω, =,P) →(Ξ,E) is a measurable function, where (Ξ,E) is the state space.Definition 2 Q :(Ξ,E) → [0, ∞] is a transition probability if Q (x, ·) isa probability measure in Ξ, andQ (·,B) is measurable, for each (x, B) ∈(Ξ × E) .Definition 3 A transition function is a family Q s,t , (s, t) ∈ I 2 ,s < t thatsatisfies for each s