## Risk-averse stochastic equilibrium problems arising in the energy industry

#### Claudia SagastizabalInstitute of Pure and Applied Mathematics (IMPA)

We consider energy markets with risk averse agents whose actions are coupled by a shared constraint, clearing the market, that couples almost surely the wait-and-see decisions of all the agents.
To solve the resulting variational inequality, with a set-valued operator, we define a sequence of approximating smoothed variational inequalities.
When the smoothing parameter goes to zero, we show convergence of the approximation scheme and by the same token, we can show existence of an equilibrium for the original risk-averse problem.
Joint work with J. P. Luna and M. Solodov

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