The allocation of construction risks between owners and their contractors has a significant impact on the total cost of construction to the owners. Previous quantitative research in this area has looked only at the negative risk aversion consequences of accepting risk, and has usually concluded that owners, being less risk averse, should accept all risk. The writers present a quantitative risk analysis model that incorporates differing risk perceptions, the positive incentive value of accepting controllable risks, and alternative incentive systems. Application of this model results in a balanced allocation of controllable and uncontrollable risks between owner and contractor in such a way that the owner's expected total cost is minimized. An example application of the model to a large mass transit construction project is presented.