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On path-independent Girsanov transform

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  • Zhang, Shuaiqi

Abstract

This article provides a unified and more direct approach to path-independent Girsanov transformation for (possibly time-inhomogeneous) Markov processes and their corresponding parabolic partial differential equations. The approach is applicable to a large class of Markov processes, including diffusion processes determined by stochastic differential equations, and Markov processes with discontinuous sample paths. In particular, we apply it to reflected diffusions, diffusions with jumps and a class of piecewise deterministic Markov processes that are Markov. The approach of this paper is also applicable to a class of time-inhomogeneous Markov processes that have jumps only at integer times, where the path-independent Girsanov transform have to be given by discontinuous but piecewise differentiable functions. In the last section of this paper, we illustrate this by a simplified stochastic model from insurance mathematics.

Suggested Citation

  • Zhang, Shuaiqi, 2021. "On path-independent Girsanov transform," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320307980
    DOI: 10.1016/j.amc.2020.125845
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    References listed on IDEAS

    as
    1. Wu, Bo & Wu, Jiang-Lun, 2018. "Characterising the path-independent property of the Girsanov density for degenerated stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 71-79.
    2. Qiao, Huijie & Wu, Jiang-Lun, 2016. "Characterizing the path-independence of the Girsanov transformation for non-Lipschitz SDEs with jumps," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 326-333.
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