Dr Kihun Nam

T: +61 3 99059892
E: kihun.nam@monash.edu

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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, K., Xu, Y. (2022) Coupled FBSDEs with measurable coefficients and its application to parabolic PDEs, Journals of Mathematical Analysis and Applications, 515(1), 126403. https://www.sciencedirect.com/science/article/abs/pii/S0022247X22004176

[2] Nam, K., Xu, Y. (2021) Forward-Backward Stochastic Equations: A Functional Fixed Point Approach, Stochastic Analysis and Applications, 1–29. https://www.tandfonline.com/doi/abs/10.1080/07362994.2021.1988857

[3] Nam, K. (2021) Locally Lipschitz BSDE driven by a continuous martingale: path- derivative approach, Stochastic Processes and their Applications, 141, 376–411. https://www.sciencedirect.com/science/article/abs/pii/S0304414921001514

[4] Fallahgoul, H., Nam, K. (2017) "Time-Changed Lévy Processes and Option Pricing: A Critical Comment". Pre-print. 2019. https://dx.doi.org/10.2139/ssrn.3226748

[5] Cheridito, P., Nam, K. (2017) "BSE's, BSDE's and fixed-point problems". Annals of Probability, 45(6A), 3795—3828. https://doi.org/10.1214/16-AOP1149