In this paper we extend the state-of-the-art stochastic programming models for the Maritime Fleet Renewal Problem (MFRP) to explicitly limit the risk of insolvency due to negative cash flows when making maritime shipping investments. This is achieved by modeling the payment of ships in a number of periodical installments rather than in a lump sum paid upfront, representing more closely the actual cash flows for a shipping company. Based on this, we propose two alternative risk control measures, where the first imposes that the cash flow in each time period is always higher than a desired threshold, while the second limits the Conditional Value-at-Risk. We test the two models on realistic test instances based on data from a shipping company. The computational study demonstrates how the two models can be used to assess the trade-offs between risk of insolvency and expected profits in the MFRP.