Comment: 18 pages, 10 figuresIn transmission expansion planning, situations can arise in which an expansion plan that is optimal for the system as a whole is detrimental to a specific country in terms of its expected economic welfare. If this country is one of the countries hosting the planned capacity expansion, it has the power to veto the plan and thus, undermine the system-wide social optimum. To solve this issue, welfare compensation mechanisms may be constructed that compensate suffering countries and make them willing to participate in the expansion plan. In the literature, welfare compensation mechanisms have been developed that work in expectation. However, in a stochastic setting, even if the welfare effect after compensation is positive in expectation, countries might still be hesitant to accept the risk that the actual, realized welfare effect may be negative in some scenarios. In this paper we analyze welfare compensation mechanisms in a stochastic setting. We consider two existing mechanisms, lump-sum payments and purchase power agreements, and we develop two novel mechanisms, based on the flow through the new transmission line and its economic value. Using a case study of the Northern European power market, we investigate how well these mechanisms succeed in mitigating risk for the countries involved. Using a theoretically ideal model-based mechanism, we show that there is a significant potential for mitigating risk through welfare compensation mechanisms. Out of the four practical mechanisms we consider, our results indicate that a mechanism based on the economic value of the new transmission line is most promising.