On the multiplicity of solutions in generation capacity investment models with incomplete markets: a risk-averse stochastic equilibrium approach

Investment in generation capacity has traditionally been evaluated by computing the present value of cashflows accruing from new equipment in a market with globally optimized capacity mix. The competition and risk that now prevail in the sector may require a more refined analysis. We consider a competitive market with agents investing in some mix of capacities: the risk exposure of a plant and the attitude towards risk of the owner depend on the plant and the portfolio of its capacities. They may also depend on hedging contracts acquired by the investor on the market if such contracts exist. We represent these effects through equilibrium models of generation capacity in incomplete markets. The models come in different versions depending on the portfolio of physical plants and hedging contracts. These modify the long-term risk of the plants, the attitude of the owners towards risk, and hence the incentive to invest. The models involve risk-averse producers and consumers, and their behavior is represented by convex risk measures. We use degree theory to prove existence and explore multiplicity of equilibrium solutions.