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A benchmark approach to risk-minimization under partial information

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  • Ceci, Claudia
  • Colaneri, Katia
  • Cretarola, Alessandra

Abstract

The goal of this paper is to investigate (locally) risk-minimizing hedging strategies under the benchmark approach in a financial semimartingale market model 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 contingent claim under partial information and provide its description in terms of the integrand in the classical Galtchouk–Kunita–Watanabe decomposition under full information via dual predictable projections. Finally we show how these results can be applied to unit-linked life insurance contracts.

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  • Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:129-146
    DOI: 10.1016/j.insmatheco.2014.01.003
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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. 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, April.
    3. Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Research Paper Series 319, Quantitative Finance Research Centre, University of Technology, Sydney.
    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. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    6. Rüdiger Frey & Wolfgang J. Runggaldier, 2001. "A Nonlinear Filtering Approach To Volatility Estimation With A View Towards High Frequency Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 199-210.
    7. 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.
    8. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    9. 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.
    10. Claudia Ceci & Anna Gerardi, 2006. "A Model For High Frequency Data Under Partial Information: A Filtering Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 555-576.
    11. 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.
    12. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    13. 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.
    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. 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.
    16. 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.
    17. 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.
    18. 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, April.
    19. Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Claudia Ceci & Anna Gerardi, 2009. "Pricing For Geometric Marked Point Processes Under Partial Information: Entropy Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 179-207.
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    Cited by:

    1. Martin Schweizer & Danijel Zivoi & Mario Šikić, 2018. "Dynamic Mean–Variance Optimization Problems With Deterministic Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, March.
    2. Alessandra Cretarola & Benedetta Salterini, 2023. "Utility-based indifference pricing of pure endowments in a Markov-modulated market model," Papers 2301.13575, arXiv.org.
    3. 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.
    4. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2015. "The F\"ollmer-Schweizer decomposition under incomplete information," Papers 1511.05465, arXiv.org, revised Mar 2016.
    5. 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.

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    More about this item

    Keywords

    Risk-minimization; Galtchouk–Kunita–Watanabe decomposition; Benchmark approach; Partial information; Unit-linked life insurance contracts; Markovian jump-diffusion models;
    All these keywords.

    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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