We analyze the general risk-neutral valuation for counterparty risk embedded in a Credit Default Swap (CDS) contract by adapting the recent findings of Brigo and Capponi (2009) to allow for simultaneous defaults among the two parties and the underlying reference credit, while the counterparty...

The index of differential-algebraic equations is one measure for the numerical problems in electric circuit simulation. The index depends on the mathematical model in different ways: setup of equations, classical or charge-oriented formulation and modelling of basic elements and semiconductor...

In electrical circuit simulation, a refined network approach is used to describe secondary and parasitic effects. This ansatz yields initial-boundary value problems of mixed partial-differential and differential-algebraic equations, so-called PDAE systems. One requirement for method-of-lines...

We present a model of opinion formation where individuals repeatedly engage in discussion and update their opinion in a social network similarly to the DeGroot model. Abstracting from the standard assumption that individuals always report their opinion truthfully, agents in our model may state...

We study a dynamic model of opinion formation in social networks. In our model, boundedly rational agents update opinions by averaging over their neighbors’ expressed opinions, but may misrepresent their own opinion by conforming or counter-conforming with their neighbors. We show that an...

We study the evolution of R&D networks in a Cournot model where firms may lower marginal costs due to bilateral R&D collaborations. Stochastically stable R&D networks exhibit the dominant group architecture, and, contrary to the existing literature, generically unique predictions about the size...

In this paper, we study a standard Cournot model where rms are able to form bilateral collaboration agreements which lower marginal cost. While a static analysis of such a model can be found in Goyal and Joshi [5], we introduce an evolutionary model. Stable networks (in the static sense) exhibit...

In this paper we show how externalities between links affect the existence and uniqueness of pairwise stable (PS) networks. For this we introduce the properties ordinal convexity (concavity) and ordinal strategic complements (substitutes) of utility functions on networks. It is shown that there...

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a...