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An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model

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  • Yu-Ting Chen
  • Cheng-Few Lee
  • Yuan-Chung Sheu

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Abstract

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Suggested Citation

  • Yu-Ting Chen & Cheng-Few Lee & Yuan-Chung Sheu, 2007. "An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model," Finance and Stochastics, Springer, vol. 11(3), pages 323-355, July.
  • Handle: RePEc:spr:finsto:v:11:y:2007:i:3:p:323-355
    DOI: 10.1007/s00780-007-0045-5
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    File URL: http://hdl.handle.net/10.1007/s00780-007-0045-5
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    References listed on IDEAS

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    1. Leland, Hayne E & Toft, Klaus Bjerre, 1996. " Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    2. A. Kyprianou & B. Surya, 2007. "Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels," Finance and Stochastics, Springer, vol. 11(1), pages 131-152, January.
    3. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
    4. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    5. Svetlana I. Boyarchenko & Sergei Z. Levendorskiĭ, 2002. "Perpetual American options," World Scientific Book Chapters,in: Non-Gaussian Merton-Black-Scholes Theory, chapter 5, pages 121-149 World Scientific Publishing Co. Pte. Ltd..
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    Citations

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    Cited by:

    1. Albrecher, Hansjörg & Constantinescu, Corina & Pirsic, Gottlieb & Regensburger, Georg & Rosenkranz, Markus, 2010. "An algebraic operator approach to the analysis of Gerber-Shiu functions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 42-51, February.
    2. repec:eee:stapro:v:127:y:2017:i:c:p:104-110 is not listed on IDEAS
    3. Chi, Yichun & Jaimungal, Sebastian & Lin, X. Sheldon, 2010. "An insurance risk model with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 52-66, February.
    4. Ming-Chi Chang & Yuan-Chung Sheu, 2013. "Free boundary problems and perpetual American strangles," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1149-1155, July.
    5. Chi, Yichun, 2010. "Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 385-396, April.
    6. Tenorio Villalón, Ángel F. & Martín Caraballo, Ana M. & Paralera Morales, Concepción & Contreras Rubio, Ignacio, 2013. "Ecuaciones diferenciales y en diferencias aplicadas a los conceptos económicos y financieros || Differential and Difference Equations Applied to Economic and Financial Concepts," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 16(1), pages 165-199, December.

    More about this item

    Keywords

    Jump-diffusion; Expected discounted penalty; Phase-type distribution; Optimal capital structure; G12; C60; C61; C65; 60J75; 91B28; 91B30; 91B70;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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