Towards a General Theory of Good-Deal Bounds*

We consider an incomplete market in the form of a multidimensional Markovian factor model, driven by a general marked point process (representing discrete jump events), as well as by a standard multidimensional Wiener process. Within this framework, we study arbitrage-free good-deal pricing bounds for derivative assets, thereby extending the results by Cochrane and Saá Requejo (2000) to the point process case, while, at the same time, obtaining a radical simplification of the theory. To illustrate, we present numerical results for the classic Merton jump-diffusion model. As a by-product of the general theory, we derive extended Hansen-Jagannathan bounds for the Sharpe Ratio process in the point process setting. *We gratefully acknowledge financial support from the Jan Wallander and Tom Hedelius foundation. We thank Anders Forsgren, Krister Svanberg, and Jan Kallsen for a number of very helpful comments. We are very grateful to Mathias Stolpe for providing us with the optimization code used in our numerical example. A number of very helpful comments from the editor and an anonymous referee has greatly improved the paper.