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A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions

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  • Luis H. R. Alvarez E.
  • Pekka Matomaki
  • Teppo A. Rakkolainen

Abstract

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated continuous diffusion process and demonstrate how this connection may be applied for characterizing the stopping policy and its value. We also establish a set of typically satisfied conditions under which increased volatility as well as higher jump-intensity decelerates rational exercise by increasing the value and expanding the continuation region.

Suggested Citation

  • Luis H. R. Alvarez E. & Pekka Matomaki & Teppo A. Rakkolainen, 2013. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Papers 1302.4181, arXiv.org.
    • Handle: RePEc:arx:papers:1302.4181
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    References listed on IDEAS

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    4. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
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    11. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
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    Cited by:

    1. Masahiko Egami & Mingxin Xu, 2009. "A continuous-time search model with job switch and jumps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 241-267, October.
    2. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
    3. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 27-58, March.
    4. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2007. "Optimal Dividend Control in Presence of Downside Risk," Discussion Papers 14, Aboa Centre for Economics.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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