On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps

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Erhan Bayraktar;
  • Subject: Mathematics - Optimization and Control | 62L15 | Quantitative Finance - Pricing of Securities | 60J75

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the stopping boundary and that it is ... View more
  • References (19)
    19 references, page 1 of 2

    [1] Larbi Alili and Andreas E. Kyprianou. Some remarks on first passage of L´evy processes, the American put and pasting principles. Ann. Appl. Probab., 15(3):2062-2080, 2005.

    [2] L. H. R. Alvarez. A class of solvable impulse control problems. Appl. Math. and Optim., 49:265-295, 2004.

    [3] Luis H. R. Alvarez. Solving optimal stopping problems of linear diffusions by applying convolution approximations. Math. Methods Oper. Res., 53(1):89-99, 2001.

    [4] E. Bayraktar and S. Sezer. Quickest detection for a Poisson process with a phase-type changetime distribution. Technical report, University of Michigan, November, 2006. Available at http://arxiv.org/PS cache/math/pdf/0611/0611563.pdf.

    [5] Erhan Bayraktar. Remarks on the perpetual American put option for jump diffusions. Technical report, University of Michigan, April, 2007. Available at http://www.citebase.org/abstract?id=oai:arXiv.org:math/0703538.

    [6] Erhan Bayraktar, Savas Dayanik, and Ioannis Karatzas. Adaptive Poisson disorder problem. Ann. Appl. Probab., 16(3):1190-1261, 2006.

    [7] Andrei N. Borodin and Paavo Salminen. Handbook of Brownian motion-facts and formulae. Probability and its Applications. Birkh¨auser Verlag, Basel, second edition, 2002.

    [8] Peter Carr. Randomization and the American put. Review of Financial Studies, 11 (3):597-626, 1998.

    [9] Savas Dayanik, H. Vincent Poor, and Semih O. Sezer. Multisource Bayesian sequential change detection. Ann. Appl. Probab., 18(2):552-590, 2008.

    [10] Erik Ekstr¨om. Perpetual American put options in a level-dependent volatility model. J. Appl. Probab., 40(3):783-789, 2003.

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