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Portfolio optimization with insider’s initial information and counterparty risk

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  • Caroline Hillairet
  • Ying Jiao

Abstract

We study the gain of an insider having private information which concerns the default risk of a counterparty. More precisely, the default time τ is modelled as the first time a stochastic process hits a random threshold L. The insider knows this threshold (as it can be the case for the manager of the counterparty) and this information is modelled by using an initial enlargement of filtration. The standard investors only observe the value of the threshold at the default time and estimate the default event by its conditional density process. The financial market consists of a risk-free asset and a risky asset whose price is exposed to a sudden jump at the default time of the counterparty. All investors aim to maximize the expected utility from terminal wealth given their own information at the initial date. We solve the optimization problem under short-selling and buying constraints and we compare through numerical illustrations the optimal processes for the insider and the standard investors. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Caroline Hillairet & Ying Jiao, 2015. "Portfolio optimization with insider’s initial information and counterparty risk," Finance and Stochastics, Springer, vol. 19(1), pages 109-134, January.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:1:p:109-134
    DOI: 10.1007/s00780-014-0246-7
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    References listed on IDEAS

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    1. Axel Grorud & Monique Pontier, 1998. "Insider Trading in a Continuous Time Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 331-347.
    2. Caroline Hillairet, 2005. "Existence Of An Equilibrium With Discontinuous Prices, Asymmetric Information, And Nontrivial Initial Σ‐Fields," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 99-117, January.
    3. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    4. Caroline Hillairet & Ying Jiao, 2012. "Credit Risk with asymmetric information on the default threshold," Post-Print hal-00663136, HAL.
    5. Caroline Hillairet & Ying Jiao, 2011. "Information Asymmetry In Pricing Of Credit Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 611-633.
    6. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
    7. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    8. 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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    Cited by:

    1. Salmerón Garrido, José Antonio & Nunno, Giulia Di & D'Auria, Bernardo, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," DES - Working Papers. Statistics and Econometrics. WS 35411, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Jos'e A. Salmer'on & Giulia Di Nunno & Bernardo D'Auria, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," Papers 2208.07163, arXiv.org, revised May 2023.
    3. Peng, Xingchun & Chen, Fenge & Wang, Wenyuan, 2021. "Robust optimal investment and reinsurance for an insurer with inside information," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 15-30.

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    More about this item

    Keywords

    Asymmetric information; Enlargement of filtrations; Counterparty risk; Optimal investment; Duality; Dynamic programming; 60H30; 91G10; 91G40; 93E20; G11; G14;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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