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Partial hedging for defaultable claims

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Advances in Mathematical Economics

Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 14))

Abstract

The subject of this paper is the problems of finding optimal hedging portfolios for defaultable claims in incomplete markets modeled by Itô processes, in the case where the portfolio processes are adapted to the full filtration. Two kinds of optimizations are considered: the maximization of the probability of super-hedge and the minimization of the expected discounted loss of hedging. We combine a super-hedging argument with Neyman–Pearson lemma in the hypothesis testing to reduce the original dynamic problems to static ones. The convex duality method as in Cvitanić and Karatzas (Bernoulli 7:79–97, 2001) plays a key role to solve the reduced problems.

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Authors and Affiliations

  1. Graduate School of Innovation Management, Tokyo Institute of Technology, 2-12-1 Ookayama, Tokyo, 152-8552, Japan

    Yumiharu Nakano

  2. PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan

    Yumiharu Nakano

Authors
  1. Yumiharu Nakano
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Correspondence to Yumiharu Nakano .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-0041, Japan

    Shigeo Kusuoka (Professor) (Professor)

  2. Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

    Toru Maruyama (Professor) (Professor)

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Nakano, Y. (2011). Partial hedging for defaultable claims. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 14. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53883-7_6

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