Large Deviations for Non-Markovian Di↵usions and a Path-Dependent Eikonal Equation
نویسندگان
چکیده
This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using backward stochastic di↵erential techniques. Similar to the Markovian case, we obtain a characterization of the action function as the unique bounded solution of a path-dependent version of the Eikonal equation. Finally, we provide an application to the short maturity asymptotics of the implied volatility surface in financial mathematics.
منابع مشابه
Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation
This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a different line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by usi...
متن کاملStochastic Differential Games in a Non-Markovian Setting
Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...
متن کاملA METHOD FOR COMPUTING DOUBLE BAND POLICIES FOR SWITCHING BETWEEN TWO DIFFUSIONS Revised Version March Running Title Optimal Switching Between Two Di usions
We develop a method for computing the optimal double band b B policy for switching between two di usions with continuous rewards and switch ing costs The two switch levels b B are obtained as perturbations of the single optimal switching point a of the control problem with no switching costs More precisely we nd that in the case of average reward problems the optimal switch levels can be obtain...
متن کاملRobustness of Zakai's Equation via Feynman-kac Representations
We propose to study the sensitivity of the optimal lter to its initialization, by looking at the distance between two di erently initialized ltering processes in terms of the ratio between two simple FeynmanKac integrals in the product space. We illustrate, by considering two simple examples, how this approach may be employed to study the asymptotic decay rate, as the di erence between the grow...
متن کاملRheological Response and Validity of Viscoelastic Model Through Propagation of Harmonic Wave in Non-Homogeneous Viscoelastic Rods
This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest....
متن کامل