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In the production of public goods, governments at different levels face different risk constraints.
This model includes risk constraints which allow finding optimal solutions within accepted risk levels.
Finally, the appropriate maintenance tasks are scheduled under the risk constraints.
In each step, the feasibility of the solution is checked against the budget and risk constraints (Fig. 4).
In contrast to chance-constrained models requiring extra binary variables, risk constraints based on CVaR only involve linear constraints and continuous variables, making it more computationally attractive.
The proposed models with risk constraints are able to avoid over-conservative solutions but still ensure system reliability represented by loss of loads.
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Fig. 1 Risk constraint and organizational form.
In order to control the system equilibrium, we adapt risk constraint techniques to handle the system imbalance uncertainty and ensure a reliable operating level.
This paper mainly focuses on maximizing the expected terminal wealth of the insurer under the risk constraint of VaR as defined in (3).
In this section, we discuss how the insurer adjusts his investment portfolio to maximize the expected terminal wealth under a risk constraint on VaR.
The system security is controlled through an overall system risk constraint, which accumulates the individual risk related to each contingency, defined as the product between the probability of contingency occurrence and the contingency severity.
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