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Optional Defaultable Markets

Machine Learning, Morgan Stanley, New York City, NY 10019, USA
Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada
Author to whom correspondence should be addressed.
The research is supported by the NSERC discovery grant 5901.
Academic Editor: Mogens Steffensen
Risks 2017, 5(4), 56;
Received: 24 September 2017 / Revised: 13 October 2017 / Accepted: 16 October 2017 / Published: 23 October 2017
PDF [427 KB, uploaded 25 October 2017]


The paper deals with defaultable markets, one of the main research areas of mathematical finance. It proposes a new approach to the theory of such markets using techniques from the calculus of optional stochastic processes on unusual probability spaces, which was not presented before. The paper is a foundation paper and contains a number of fundamental results on modeling of defaultable markets, pricing and hedging of defaultable claims and results on the probability of default under such conditions. Moreover, several important examples are presented: a new pricing formula for a defaultable bond and a new pricing formula for credit default swap. Furthermore, some results on the absence of arbitrage for markets on unusual probability spaces and markets with default are also provided. View Full-Text
Keywords: defaultable claims; hazard process; martingale deflators; optional processes; hedging defaultable claims; hazard process; martingale deflators; optional processes; hedging
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Abdelghani, M.N.; Melnikov, A.V. Optional Defaultable Markets. Risks 2017, 5, 56.

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