The outline of this paper is as follows. Section 2 presents the financial market model. Section 3 gives a brief description of the martingale representation theo- rem in our pure jump context, which is used to generate our completeness results later. Self-financing strategies and the budget constraint are described in detail in Sect. 4. The finite horizon problem is formulated and solved in Sect. 5, while Sect. 6 considers the infinite horizon problem. The completeness of markets with respect to trading strategies is discussed in Sect. 7. Explicit solutions for the case of HARA utility are presented in Sect. 8. Closed form solutions for the context of VG.
