We analyze the 2 × 2 nonhomogeneous relativistic Euler equations for perfect fluids in special relativity. We impose appropriate conditions on the lower order source terms and establish the existence of global entropy solutions of the Cauchy problem under these conditions.
We study a three-firm contagion model with counterparty risk and apply this model to price defaultable bonds and credit default swap (CDS). This model assumes that default intensities are driven by external common factors as well as other defaults in the system. Using the “total hazard” approach, default times can be generated and the joint density function is obtained. We represent the pricing method of defaultable bonds and obtain the closed-form pricing formulas. By the approach of “change of measure,” analytical solutions of CDS swap rate (swap premuim) are derived in the continuous time framework and the discrete time framework, respectively.
In this paper two classes of large supergames, i.e., infinitely repeated games played by many players on 2-dimensional rectangle lattice are studied. Each person located on the vertices of the lattice plays four 4-person team games or 4-person 2-pairs team games simultaneously with her neighbors. Under the conditions of the pre-specified updating rules and the transition probabilities, the strategy process forms a Markov Chain. The formula of invariant measures which represent the long-run equilibrium plays with symmetric payoffs are obtained.
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