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Shot-noise processes and the minimal martingale measure

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  • Schmidt, Thorsten
  • Stute, Winfried

Abstract

This article proposes a model for stock prices which incorporates shot-noise effects. This means, that sudden jumps in the stock price are allowed, but their effect may decline as time passes by. Our model is general enough to capture arbitrary effects of this type. Generalizing previous approaches to shot noise we in particular allow the decay to be stochastic. This model describes an incomplete market, so that the martingale measure is not unique. We derive the minimal martingale measure via continuous time methods.

Suggested Citation

  • Schmidt, Thorsten & Stute, Winfried, 2007. "Shot-noise processes and the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1332-1338, July.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:12:p:1332-1338
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    References listed on IDEAS

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    1. Gaspar, Raquel M. & Schmidt, Thorsten, 2005. "Quadratic Portfolio Credit Risk models with Shot-noise Effects," SSE/EFI Working Paper Series in Economics and Finance 616, Stockholm School of Economics.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Junna Bi & Junyi Guo, 2013. "Optimal Mean-Variance Problem with Constrained Controls in a Jump-Diffusion Financial Market for an Insurer," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 252-275, April.
    2. Thorsten Schmidt & Alexander Novikov, 2008. "A Structural Model with Unobserved Default Boundary," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 183-203.
    3. Li, Xiaohu & Wu, Jintang, 2014. "Asymptotic tail behavior of Poisson shot-noise processes with interdependence between shock and arrival time," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 15-26.
    4. Yan, Jun, 2017. "Deviations and asymptotic behavior of convex and coherent entropic risk measures for compound Poisson process influenced by jump times," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 71-79.
    5. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, vol. 2(1), pages 1-22, February.
    6. Kai Kopperschmidt & Winfried Stute, 2009. "Purchase timing models in marketing: a review," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(2), pages 123-149, June.
    7. Liang, Xiaoqing & Lu, Yi, 2017. "Indifference pricing of a life insurance portfolio with risky asset driven by a shot-noise process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 119-132.

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