Research field: Mathematical AI, Stochastic differential equations
Professor: Donghyun Kim
Research description:
My research focuses on mathematical AI and stochastic differential equations (SDEs), with primary applications in mathematical finance.
Classical Black-Scholes models are expressed as SDEs and are invaluable for modeling the dynamics of risky assets.
Furthermore, I study a range of stochastic volatility models that capture distinctive features in options data and examine their implications for pricing and risk management. Under the stochastic volatility model, the associated pricing problems often convert to singularly perturbed partial differential equations, for which closed-form solutions are rare, motivating asymptotic and numerical approximation methods. I further leverage deep learning to improve the accuracy and robustness of these approximations.