A design of anautomatic network capacity markets, oftenreferred to as a bandwidth market, is presented. Three topicsare investigated. First, a network model is proposed. Theproposed model is based upon a trisection of the participantroles into network users, network owners, and market middlemen.The network capacity is defined in a way that allows it to betraded, and to have a well defined price. The network devicesare modeled as core nodes, access nodes, and border nodes.Requirements on these are given. It is shown how theirfunctionalities can be implemented in a network. Second, asimulated capacity market is presented, and a statisticalmethod for estimating the price dynamics in the market isproposed. A method for pricing network services based on sharedcapacity is proposed, in which the price of a service isequivalent to that of a financial derivative contract on anumber of simple capacity shares.Third, protocols for theinteraction between the participants are proposed. The marketparticipants need to commit to contracts with an auditableprotocol with a small overhead. The proposed protocol is basedon a public key infrastructure and on known protocols for multiparty contract signing. The proposed model allows networkcapacity to be traded in a manner that utilizes the networkeciently. A new feature of this market model, compared to othernetwork capacity markets, is that the prices are not controlledby the network owners. It is the end-users who, by middlemen,trade capacity among each-other. Therefore, financial, ratherthan control theoretic, methods are used for the pricing ofcapacity. <b>Keywords:</b>Computer network architecture, bandwidthtrading, inter-domain Quality-of-Service, pricing,combinatorial allocation, financial derivative pricing,stochastic modeling

<p>A design of anautomatic network capacity markets, oftenreferred to as a bandwidth market, is presented. Three topicsare investigated. First, a network model is proposed. Theproposed model is based upon a trisection of the participantroles into network users, network owners, and market middlemen.The network capacity is defined in a way that allows it to betraded, and to have a well defined price. The network devicesare modeled as core nodes, access nodes, and border nodes.Requirements on these are given. It is shown how theirfunctionalities can be implemented in a network. Second, asimulated capacity market is presented, and a statisticalmethod for estimating the price dynamics in the market isproposed. A method for pricing network services based on sharedcapacity is proposed, in which the price of a service isequivalent to that of a financial derivative contract on anumber of simple capacity shares.Third, protocols for theinteraction between the participants are proposed. The marketparticipants need to commit to contracts with an auditableprotocol with a small overhead. The proposed protocol is basedon a public key infrastructure and on known protocols for multiparty contract signing. The proposed model allows networkcapacity to be traded in a manner that utilizes the networkeciently. A new feature of this market model, compared to othernetwork capacity markets, is that the prices are not controlledby the network owners. It is the end-users who, by middlemen,trade capacity among each-other. Therefore, financial, ratherthan control theoretic, methods are used for the pricing ofcapacity.</p><p><b>Keywords:</b>Computer network architecture, bandwidthtrading, inter-domain Quality-of-Service, pricing,combinatorial allocation, financial derivative pricing,stochastic modeling</p>

We develop expansion methods as a new computational approach towards high-dimensional partial differential equations (PDEs), particularly of such type as arising in the valuation of financial derivatives. The proposed methods are extended from [41] and use principal component analysis (PCA) of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. They enable calculation of highly accurate approximate solutions with computational complexity polynomial in the number of dimensions for PDEs with a low number of dominant principal components. For the case of PDEs with constant coefficients, we show existence of expansion solutions and prove theoretical error bounds. We give a precise characterisation of when our methods can be applied and construct specific examples of a first and second order version. We provide numerical results showing that the empirically observed convergence speeds are in agreement with the theoretical predictions. For the case of PDEs with varying coefficients, we give a heuristic motivation using the Parametrix approach and empirically test the methods' accuracy for a range of variable parameter stock models. We demonstrate the applicability of our expansion methods to real-world securities pricing problems by considering path-dependent and early-exercise options in the LIBOR market model. Using the example of Bermudan swaptions and Ratchet floors, which are considered difficult benchmark problems, we give a careful analysis of the numerical accuracy and computational complexity. We are able to demonstrate that for problems with medium to high dimensionality, around 60-100, and moderate time horizons, the presented PDE methods deliver results comparable in accuracy to benchmark state-of-the-art Monte Carlo methods in similar or (significantly) faster run time.