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Information and optimal investment in defaultable assets

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  • Giulia Di Nunno
  • Steffen Sjursen

Abstract

We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modelled via a counting process in line with large part of the literature in credit risk. In order to deal with both cases of inside and partial information we consider the framework of the anticipating calculus of forward integration. This does not require a priori assumptions typical of the framework of enlargement of filtrations. We find necessary and sufficient conditions for the existence of a locally maximizing portfolio of the expected utility at terminal time. We consider a large class of utility functions. In addition we show that the existence of the solution implies the semi-martingale property of the noises driving the stock. Some discussion on unicity of the maxima is included.

Suggested Citation

  • Giulia Di Nunno & Steffen Sjursen, 2013. "Information and optimal investment in defaultable assets," Papers 1312.6032, arXiv.org.
  • Handle: RePEc:arx:papers:1312.6032
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    File URL: http://arxiv.org/pdf/1312.6032
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    References listed on IDEAS

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    1. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    2. Delia Coculescu & Monique Jeanblanc & Ashkan Nikeghbali, 2012. "Default times, no-arbitrage conditions and changes of probability measures," Finance and Stochastics, Springer, vol. 16(3), pages 513-535, July.
    3. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    4. Pham, Huyên, 2010. "Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1795-1820, August.
    5. repec:dau:papers:123456789/1803 is not listed on IDEAS
    6. Tomasz Bielecki & Inwon Jang, 2006. "Portfolio optimization with a defaultable security," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(2), pages 113-127, June.
    7. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2010. "What happens after a default: The conditional density approach," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1011-1032, July.
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