Summary: 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 J. Cochrane and J. Saá Requejo [“Beyond arbitrage: good-deal asset price bounds in incomplete markets”, J. Political Econ. 108, 79–119 (2000; doi:10.1086/262112)] 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.