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A market with defaultable bonds where the bond dynamics is in aHeath-Jarrow-Morton setting and the forward rates are driven by an infinitenumber of Levy factors is considered. The setting includes rating migrationsdriven by a Markov chain. All basic types of recovery are investigated. Weformulate necessary and sufficient conditions (generalized HJM conditions)under which the market is arbitrage free. Connections with consistencyconditions are discussed.

Defaultable bonds with an infinite number of Levy factors