My research interest includes stochastic calculus, stochastic differential equations, and related applications in quantitative finance. Specifically, I work in the Malliavin calculus of Brownian motion, fractional Brownian motion, and Lévy processes. We establish new series representations of martingales, which are widely applicable in pricing and hedging problems in finance. I also study stochastic differential equations driven by non-Markovian time-changed Brownian motion and the approximation schemes for their solutions.
Scholarly Work
Sixian Jin, Qidi Peng and Henry Schellhorn. Fractional Hida-Malliavin derivatives and series representations of fractional conditional expectations. Communications on Stochastic Analysis, 9(2):213-238, 2015.
Hongyi Chen (undergraduate), Sixian Jin and Di Kang. Pricing the zero-coupon bond of the extended Cox-Ingersoll-Ross model using Malliavin calculus. Submitted, arXiv:2010.01697.
Sixian Jin and Kei Kobayashi. Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators. BIT Numerical Mathematics, 61(3):829-857,2021.
Sixian Jin, Henry Schellhorn and Josep Vives. Dyson type formula for pure jump L\'{e}vy processes and applications. Stochastic Processes and their Applications, 130(2):824-844, 2020.
Sixian Jin and Kei Kobayashi. Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients. Journal of Mathematical Analysis and Applications, 476(2):619-636, 2019.
Sixian Jin, Qidi Peng and Henry Schellhorn. Estimation of the pointwise Holder exponent of hidden multifractional Brownian motion using
wavelet coefficients. Statistical Inference for Stochastic Processes, 21(1):113–140, 2018.
