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Dependent defaults and credit migrations

Tomasz R. Bielecki;  Marek Rutkowski — 2003

Applicationes Mathematicae

The paper deals with the modelling of mutually dependent default times of several credit names through the intensity-based approach. We extend to the case of multiple ratings some previous results due to Schmidt (1998), Kusuoka (1999) and Jarrow and Yu (2001). The issue of the arbitrage valuation of simple basket credit derivatives is also briefly examined. We argue that our approach leads, in some cases, to a significant reduction of the dimensionality of the valuation problem at hand.

Conditional Markov chains - construction and properties

Tomasz R. Bielecki;  Jacek Jakubowski;  Mariusz Niewęgłowski — 2015

Banach Center Publications

In this paper we study finite state conditional Markov chains (CMCs). We give two examples of CMCs, one which admits intensity, and another one, which does not admit an intensity. We also give a sufficient condition under which a doubly stochastic Markov chain is a CMC. In addition we provide a method for construction of conditional Markov chains via change of measure.

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