Dr Kihun Nam

Research Overview

My research focus is backward stochastic differential equations (BSDEs), which appear in optimal controls of dynamic random systems. In addition to traditional applications such as stochastic control and financial derivative pricing, Multidimensional Superlinear BSDEs, which is of my main focus, can be used to investigate the following problems: the price of financial derivatives, price-impact models, x-value adjustment (xVA), Nash equilibrium of the stochastic differential game, mean-field game theory, and Machine-learning algorithm for parabolic PDEs. I also have a general interest in various area of stochastic analysis such as time-changed Levy process, dynamic random graph, and mathematical neuroscience.

Selected Publications

[1] Nam, Kihun. "Global Well-posedness of Non-Markovian Multidimensional Superquadratic BSDE". Pre-print. 2020. https://arxiv.org/abs/1912.03692

[2] Fallahgoul, Hasan ; Nam, Kihun. "Time-Changed Lévy Processes and Option Pricing: A Critical Comment". Pre-print. 2019. https://dx.doi.org/10.2139/ssrn.3226748

[3] Cheridito, Patrick ; Nam, Kihun. "Bse'S, Bsde'S and fixed-point problems". In: Annals of Probability. 2017 ; Vol. 45, No. 6A. pp. 3795-3828. https://doi.org/10.1214/16-AOP1149

[4] Cheridito, Patrick ; Nam, Kihun. "Multidimensional quadratic and subquadratic BSDEs with special structure". In: Stochastics: An International Journal of Probability and Stochastic Processes. 2015 ; Vol. 87, No. 5. pp. 871-884. https://doi.org/10.1080/17442508.2015.1013959

[5] Cheridito, Patrick ; Nam, Kihun. "BSDEs with terminal conditions that have bounded Malliavin derivative". In: Journal of Functional Analysis. 2014 ; Vol. 266, No. 3. pp. 1257-1285. https://doi.org/10.1016/j.jfa.2013.12.004