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The dynamical evolution of many economic, sociological, biological, and physical systems tends to be dominated by a relatively small number of unexpected, large changes ("extreme events"). We study the large, internal changes produced in a generic multiagent population competing for a limited resource, and find that the level of predictability increases(More)
We study N-player continuous-time Cournot games in an oligopoly where firms choose production quantities. These are nonzero-sum differential games, whose value functions may be characterized by systems of nonlinear Hamilton-Jacobi partial differential equations. When resources are in finite supply, such as oil, exhaustibility enters as boundary conditions(More)
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain " communities " of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we(More)
  • Björn Gustafsson, Alexander Vasil 'ev, Stockholm-Valparaíso, Great Britain, J R Ockendon, S D Howison +19 others
  • 2004
Preface One of the most influential works in Fluid Dynamics at the edge of the 19-th century was a short paper [130] written by Henry Selby Hele-Shaw (1854–1941). There Hele-Shaw first described his famous cell that became a subject of deep investigation only more than 50 years later. A Hele-Shaw cell is a device for investigating two-dimensional flow of a(More)
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain " communities " of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we(More)
We consider the pricing of volatility products and especially volatility and variance swaps. Under risk-neutral valuation we provide closed form formulae for volatility-average and variance swaps. Also we provide a general partial differential equation for derivatives that have an extra dependence on an average of the volatility. We give approximate(More)