Problem 1. Consider a model of a financial market with d +1 assets in discrete time on a finite probability space. Standard notation from the lecture notes is used. (a) [7 points] Give the definition of self-financing trading strategy, and provide an example of a process that satisfies the self-financing condition but is not predictable. (b) (10 points) Prove that there exists a bijection between the set of Rl+d- valued self-financing trading strategies {H = (H, H)} and the set of pairs {(V., H)}, with V, an Fo-measurable random variable and H an Rd-valued predictable process. (b) [8 points) Determine whether it is true or not that = o + ( )for all te {0, 1, ...,T}. Problem 1. Consider a model of a financial market with d +1 assets in discrete time on a finite probability space. Standard notation from the lecture notes is used. (a) [7 points] Give the definition of self-financing trading strategy, and provide an example of a process that satisfies the self-financing condition but is not predictable. (b) (10 points) Prove that there exists a bijection between the set of Rl+d- valued self-financing trading strategies {H = (H, H)} and the set of pairs {(V., H)}, with V, an Fo-measurable random variable and H an Rd-valued predictable process. (b) [8 points) Determine whether it is true or not that = o + ( )for all te {0, 1, ...,T}