Battery participants in performance-based frequency regulation markets must consider the cost of battery aging in their operating strategies to maximize market profits. In this paper we solve this problem by proposing an optimal control policy and an optimal bidding policy based on realistic market settings and an accurate battery aging model. The proposed control policy has a threshold structure and achieves near-optimal performance with respect to an offline controller that has complete future information. The proposed bidding policy considers the optimal control policy to maximize market profits while satisfying the market performance requirement through a chance-constraint. It factors the value of performance and supports a trade-off between higher profits and a lower risk of violating performance requirements. We demonstrate the optimality of both policies using simulations. A case study based on the PJM regulation market shows that our approach is effective at maximizing operating profits. Index Terms-Battery energy storage, degradation, frequency regulation, power system economics NOMENCLATURE A. Parameters and Variables B Battery energy storage power rating in MW b t Battery dispatch power during t in MW b The set of all battery dispatch power b = {b t } C Regulation capacity in MW C Maximum regulation capacity E Battery energy storage capacity in MWh E, E Upper and lower energy limit for the battery energy storage in MWh E g t , E g t Upper and lower energy limit enforced by the control policy g during interval t in MWh e t Battery energy level during t in MWh e The set of all battery energy levels e = {e t } e max t , e min t Maximum and minimum energy level up to interval t in MWh g Control policy for the battery energy storage i Index of identified cycles j Index of regulation capacity bid segments J Number of total bid segments M Duration of one dispatch interval in hours R Battery cell replacement price in $/MWh r t Normalized regulation instruction during t r The set of all normalized regulation instructions r = {r t } The authors are with the