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A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Lévy factors is considered. The setting includes rating migrations driven by a Markov chain. All basic types of recovery are investigated. We formulate necessary and sufficient conditions (generalized HJM conditions) under which the market is arbitrage-free. Connections with consistency conditions are discussed.
Different kinds of renewal equations repeatedly arise in connection
with renewal risk models and variations. It is often appropriate to
utilize bounds instead of the general solution to the renewal
equation due to the inherent complexity. For this reason, as a first
approach to construction of bounds we employ a general Lundberg-type
methodology. Second, we focus specifically on exponential bounds
which have the advantageous feature of being closely connected to
the asymptotic behavior (for large...
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