Fisheries management must address multiple, often conflicting objectives in a highly uncertain context. In particular, while the bio-economic performance of trawl fisheries is subject to high levels of biological and economic uncertainty, the impact of trawling on broader biodiversity is also a major concern for their management. The purpose of this study is to propose an analytical framework to formally assess the trade-offs associated with balancing biological, economic and non-target species conservation objectives. We use the Australian Northern Prawn Fishery (NPF), which is one of the most valuable federally managed commercial fisheries in Australia, as a case study. We develop a stochastic co-viability assessment of the fishery under multiple management objectives. Results show that, due to the variability in the interactions between the fishery and the ecosystem, current management strategies are characterized by biological and economic risks. Results highlight the trade-offs between respecting biological, economic and non-target species conservation constraints at each point in time with a high probability and maximizing the net present value of the fishery.