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A Benchmark Approach to Risk-Minimization under Partial Information

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  • Claudia Ceci
  • Katia Colaneri
  • Alessandra Cretarola

Abstract

In this paper we study a risk-minimizing hedging problem for a semimartingale incomplete financial market where d+1 assets are traded continuously and whose price is expressed in units of the num\'{e}raire portfolio. According to the so-called benchmark approach, we investigate the (benchmarked) risk-minimizing strategy in the case where there are restrictions on the available information. More precisely, we characterize the optimal strategy as the integrand appearing in the Galtchouk-Kunita-Watanabe decomposition of the benchmarked claim under partial information and provide its description in terms of the integrands in the classical Galtchouk-Kunita-Watanabe decomposition under full information via dual predictable projections. Finally, we apply the results in the case of a Markovian jump-diffusion driven market model where the assets prices dynamics depend on a stochastic factor which is not observable by investors.

Suggested Citation

  • Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2013. "A Benchmark Approach to Risk-Minimization under Partial Information," Papers 1307.6036, arXiv.org.
  • Handle: RePEc:arx:papers:1307.6036
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    References listed on IDEAS

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    1. Thomas Møller, 2001. "Risk-minimizing hedging strategies for insurance payment processes," Finance and Stochastics, Springer, vol. 5(4), pages 419-446.
    2. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    3. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
    4. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    5. Hardy Hulley & Martin Schweizer, 2010. "M6 - On Minimal Market Models and Minimal Martingale Measures," Research Paper Series 280, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    7. Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Papers 1210.2337, arXiv.org.
    8. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    9. Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
    10. Ceci, Claudia & Cretarola, Alessandra & Russo, Francesco, 2014. "BSDEs under partial information and financial applications," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2628-2653.
    11. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Martin Schweizer, 1994. "Risk-Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342.
    13. Rüdiger Frey, 2000. "Risk Minimization with Incomplete Information in a Model for High-Frequency Data," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 215-225.
    14. Constantinos Kardaras, 2012. "Market viability via absence of arbitrage of the first kind," Finance and Stochastics, Springer, vol. 16(4), pages 651-667, October.
    15. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Riesner, Martin, 2006. "Hedging life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 599-608, June.
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    Cited by:

    1. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2015. "Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 47-60.
    2. Jan Baldeaux & Fung & Katja Ignatieva & Eckhard Platen, 2015. "A Hybrid Model for Pricing and Hedging of Long-dated Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(4), pages 366-398, September.
    3. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2015. "The F\"ollmer-Schweizer decomposition under incomplete information," Papers 1511.05465, arXiv.org, revised Mar 2016.

    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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