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Local Risk-Minimization under the Benchmark Approach

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  • Francesca Biagini
  • Alessandra Cretarola
  • Eckhard Platen

Abstract

We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extremely weak assumptions a much richer modeling world than the classical methodology.

Suggested Citation

  • Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Papers 1210.2337, arXiv.org.
  • Handle: RePEc:arx:papers:1210.2337
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    References listed on IDEAS

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    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    2. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
    3. 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.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    5. 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.
    6. 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.
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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. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2.
    3. Ke Du & Eckhard Platen, 2016. "Benchmarked Risk Minimization," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 617-637, July.
    4. 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.
    5. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Research Paper Series 379, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Francesca Biagini & Andreas Groll & Jan Widenmann, 2016. "Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-26, July.
    7. Alessandro Gnoatto & Martino Grasselli & Eckhard Platen, 2016. "A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds," Research Paper Series 374, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. repec:wsi:ijtafx:v:15:y:2012:i:04:n:s0219024912500252 is not listed on IDEAS
    9. Francesca Biagini & Yinglin Zhang, 2016. "Polynomial Diffusion Models for Life Insurance Liabilities," Papers 1602.07910, arXiv.org, revised Sep 2016.

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