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Ma, Jin; Ren, Zhenjie; Touzi, Nizar; Zhang, Jianfeng

Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation. (English. French summary) Zbl 1351.35276

Ann. Inst. Henri Poincaré, Probab. Stat. 52, No. 3, 1196-1216 (2016).
By adapting a PDE method to path-dependent equations and using techniques of backward stochastic differential equations, the large deviation pronciple (LDP) is established for a class of stochastic differential equations driven by Brownian motion with path-dependent Lipschitzian coefficientsm. This provides an alternative study of the topic to F. Gao and J. Liu [Stoch. Dyn. 6, No. 4, 487–520 (2006; Zbl 1113.60030)] where the pioneering idea of Freidlin and Wentzell is applied. The main result is applied to characterize the short maturity asymptotics of the implied volatility surface in financial mathematics.
Reviewer: Feng-Yu Wang (Swansea)

Cited in 5 Documents

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
35D40 Viscosity solutions to PDEs
35K10 Second-order parabolic equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)

Keywords:

large deviations; backward stochastic differential equations; viscosity solutions of path-dependent PDEs

Citations:

Zbl 1113.60030
Cite Review PDF
Full Text: DOI arXiv Euclid

References:

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