We study the effects of market incompleteness on speculation, investor survival, and asset pricing moments when investors disagree about the likelihood of jumps and have recursive preferences. We consider two models. In a model with jumps in aggregate consumption, incompleteness barely matters because the consumption claim resembles an insurance product against jump risk and effectively reproduces approximate spanning. In a long-run risk model with jumps in the long-run growth rate, market incompleteness affects speculation and investor survival. Jump and diffusive risks are more balanced regarding their importance, and therefore the consumption claim cannot reproduce approximate spanning.