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Approximations of non-smooth integral type functionals of one dimensional diffusion processes

Author

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  • Kohatsu-Higa, A.
  • Makhlouf, A.
  • Ngo, H.L.

Abstract

In this article, we obtain the weak and strong rates of convergence of time integrals of non-smooth functions of a one dimensional diffusion process. We propose the use of the exact simulation scheme to simulate the process at discretization points. In particular, we also present the rates of convergence for the weak and strong errors of approximation for the local time of a one dimensional diffusion process as an application of our method.

Suggested Citation

  • Kohatsu-Higa, A. & Makhlouf, A. & Ngo, H.L., 2014. "Approximations of non-smooth integral type functionals of one dimensional diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1881-1909.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:5:p:1881-1909
    DOI: 10.1016/j.spa.2014.01.003
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    References listed on IDEAS

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    1. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
    2. Erhan Bayraktar & Virginia Young, 2010. "Optimal investment strategy to minimize occupation time," Annals of Operations Research, Springer, vol. 176(1), pages 389-408, April.
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    Cited by:

    1. Kulik, Alexei M., 2019. "On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 473-506.
    2. Altmeyer, Randolf & Chorowski, Jakub, 2018. "Estimation error for occupation time functionals of stationary Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1830-1848.
    3. Altmeyer, Randolf, 2023. "Central limit theorems for discretized occupation time functionals," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 101-125.

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