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Time homogeneous diffusion with drift and killing to meet a given marginal

Author

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  • Noble, John M.

Abstract

In this article, it is proved that for any probability law μ over R and a drift field b:R→R and killing field k:R→R+ which satisfy hypotheses stated in the article and a given terminal time t>0, there exists a string m, an α∈(0,1], an initial condition x0∈R and a process X with infinitesimal generator (12∂2∂m∂x+b∂∂m−∂K∂m) where k=∂K∂x such that for any Borel set B∈B(R), P(Xt∈B|X0=x0)=αμ(B). Firstly, it is shown the problem with drift and without killing can be accommodated, after a simple co-ordinate change, entirely by the proof in Noble (2013). The killing field presents additional problems and the proofs follow the lines of Noble (2013) with additional arguments.

Suggested Citation

  • Noble, John M., 2015. "Time homogeneous diffusion with drift and killing to meet a given marginal," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1500-1540.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1500-1540
    DOI: 10.1016/j.spa.2014.11.006
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    References listed on IDEAS

    as
    1. Noble, John M., 2013. "Time homogeneous diffusions with a given marginal at a deterministic time," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 675-718.
    2. Forde, Martin, 2011. "A diffusion-type process with a given joint law for the terminal level and supremum at an independent exponential time," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2802-2817.
    3. Peter Carr & Sergey Nadtochiy, 2017. "Local Variance Gamma And Explicit Calibration To Option Prices," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 151-193, January.
    Full references (including those not matched with items on IDEAS)

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