Using a Grid for Risk Management: CommunicationComplexity of Covariance Calculations

Risk management has evolved as one of the key success factors for enterprises especially in the financial services industry. Itis highly demanding in terms of business requirements and technical resources, making it an almost ideal application fordistributed computing concepts like e.g. grid computing. In this paper we focus on a specific problem—the estimation ofcovariance matrices that provide a powerful tool for decisions on investments. In this context we analyze different networktopologies that the corresponding calculations can be performed on. We derive complexity classes for a distributedcalculation scenario on these topologies. As a general result we find an upper and lower bound for the complexity of adistributed calculation in an arbitrary network structure. These results not only provide a different view on grid resourceallocation but also make a contribution towards better understanding the business value of grid computing....