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Incompleteness of markets driven by a mixed diffusion

Author

Listed:
  • N. Bellamy

    (Equipe d'analyse et probabilitÊs, UniversitÊ d'Evry Val d'Essonne, Boulevard des coquibus, F-91025 Evry Cedex, France Manuscript)

  • M. Jeanblanc

    (Equipe d'analyse et probabilitÊs, UniversitÊ d'Evry Val d'Essonne, Boulevard des coquibus, F-91025 Evry Cedex, France Manuscript)

Abstract

An incomplete market driven by a pair of Wiener and Poisson processes is considered. The range of European and American claim prices is determined.

Suggested Citation

  • N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:209-222
    Note: received: July 1997; final version received: April 1999
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    Citations

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    Cited by:

    1. Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.
    2. Erik Ekstrom & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526, arXiv.org.
    3. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    4. Bellamy, Nadine, 2001. "Wealth optimization in an incomplete market driven by a jump-diffusion process," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 259-287, April.
    5. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    6. Laura Pasin & Tiziano Vargiolu, 2010. "Optimal Portfolio for CRRA Utility Functions when Risky Assets are Exponential Additive Processes," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(1‐2), pages 65-90, February.
    7. Leonel Perez-hernandez, 2007. "On the existence of an efficient hedge for an American contingent claim within a discrete time market," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 547-551.
    8. Erik Ekstrom & Johan Tysk, 2007. "Convexity theory for the term structure equation," Papers math/0702435, arXiv.org.
    9. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    10. Xavier De Scheemaekere, 2009. "Upper and lower bounds on dynamic risk indifference prices in incomplete markets," Papers 0909.3219, arXiv.org, revised Sep 2010.
    11. Branger, Nicole & Mahayni, Antje, 2006. "Tractable hedging: An implementation of robust hedging strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 1937-1962, November.
    12. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
    13. Bergenthum Jan & Rüschendorf Ludger, 2008. "Comparison results for path-dependent options," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 53-72, March.
    14. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.
    15. George M. Mukupa & Elias R. Offen, 2020. "The Semimartingale Equilibrium Risk Premium for a Risk Seeking Investor," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(4), pages 1-13, August.
    16. Nikita Ratanov, 2016. "Option Pricing Under Jump-Diffusion Processes with Regime Switching," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 829-845, September.
    17. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    18. Erik Ekstrom & Johan Tysk, 2005. "Properties of option prices in models with jumps," Papers math/0509232, arXiv.org, revised Nov 2005.
    19. Luciano Campi & Simon Polbennikov & Sbuelz, 2005. "Assessing Credit with Equity: A CEV Model with Jump to Default," Working Papers 24/2005, University of Verona, Department of Economics.
    20. Leonel Pérez-Hernández, 2005. "On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market," Department of Economics and Finance Working Papers EC200505, Universidad de Guanajuato, Department of Economics and Finance.

    More about this item

    Keywords

    Contingent claim valuation; incomplete model; martingale measures; Black and Scholes function;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

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