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Optimization problem and mean variance hedging on defaultable claims

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  • Stephane Goutte
  • Armand Ngoupeyou

Abstract

We study the pricing and the hedging of claim {\psi} which depends on the default times of two firms A and B. In fact, we assume that, in the market, we can not buy or sell any defaultable bond of the firm B but we can only trade defaultable bond of the firm A. Our aim is then to find the best price and hedging of {\psi} using only bond of the firm A. Hence, we solve this problem in two cases: firstly in a Markov framework using indifference price and solving a system of Hamilton-Jacobi-Bellman equations, secondly, in a more general framework, using the mean variance hedging approach and solving backward stochastic differential equations (BSDE).

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File URL: http://arxiv.org/pdf/1209.5953
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Paper provided by arXiv.org in its series Papers with number 1209.5953.

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Date of creation: Sep 2012
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Handle: RePEc:arx:papers:1209.5953

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  1. Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
  2. Gourieroux, Christian & Laurent, Jean-Paul & Pham, Huyên, 1996. "Mean-variance hedging and numeraire," CEPREMAP Working Papers (Couverture Orange) 9611, CEPREMAP.
  3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, American Finance Association, vol. 29(2), pages 449-70, May.
  4. St\'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
  5. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
  6. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(2), pages 259-276.
  7. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(2), pages 99-123.
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