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Local Risk-Minimization under the Benchmark Approach

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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.

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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp319.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 319.

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Length: 34
Date of creation: 01 Dec 2012
Date of revision:
Handle: RePEc:uts:rpaper:319

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Keywords: local risk-minimization; Follmer-Schweizer decomposion; Galtchouck-Kunita-Watanabe decomposion; numeraire portfolio; benchmark approach; real world pricing; martingale representation;

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References

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  1. 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.
  2. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 1-22, March.
  4. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  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. 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.
  7. Francesca Biagini & Jan Widenmann, 2012. "Pricing Of Unemployment Insurance Products With Doubly Stochastic Markov Chains," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1250025-1-1.
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Cited by:
  1. 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.
  2. Francesca Biagini & Jan Widenmann, 2012. "Pricing Of Unemployment Insurance Products With Doubly Stochastic Markov Chains," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1250025-1-1.

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