Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation (Q330697)
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scientific article; zbMATH DE number 6643516
| Language | Label | Description | Also known as |
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| English | Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation |
scientific article; zbMATH DE number 6643516 |
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Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation (English)
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26 October 2016
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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 \textit{F. Gao} and \textit{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.
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large deviations
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backward stochastic differential equations
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viscosity solutions of path-dependent PDEs
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