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Cognitive radio will enable terminals with access to licensed and unlicensed portions of the spectrum. This feature is expected to solve bandwidth scarcity problems in future wireless networks. However, different parts of the spectrum will be subject not only to different propagation conditions, but also to different licensing and billing agreements. Therefore, in order to obtain the major profit and spectrum efficiency, resource allocation algorithms must now target both network and economic performance metrics. This problem can be conveniently expressed as a multi-objective portfolio optimization problem, which has been studied in detail in the field of economics. This paper addresses the study of network and economic Pareto optimal trade-off performance regions of cognitive radio systems under average transmit power control policies. Each packet transmission in primary and secondary mode is regarded as a financial asset whose average transmit power is optimized so as to simultaneously maximize return and minimize risk, where risk is the variance of the return. This paper studies three types of Pareto optimal trade-off regions: primary vs. secondary throughput, return vs. risk, and sum-throughput vs. fairness, where fairness is evaluated by means of the Gini index. The boundaries of these trade-off regions are derived in parametric closed-form expressions. A power control policy is further proposed that maximizes return while simultaneously controlling risk and ensuring a level of quality of service for primary and secondary users. This means that operators can maximize revenue and network efficiency, while simultaneously minimizing risk and also ensuring fairness between primary and secondary users.

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