Research at FAST

83 Department of Applied Mathematics Department of Applied Mathematics Representative Publications • Mathematics of Operations Research, 2020 • SIAM Journal on Control and Optimization, 58(4), 2078-2113, 2020 • SIAM Journal on Control and Optimization, 55(6), 3833-3868, 2017 Dr FU Guanxing Assistant Professor Research Overview I am mostly interested in the interface between mean field games, stochastic control, applied probability, with applications in finance and economics. Theoretically, I develop mathematical tools from a probabilistic point of view to establish the existence results of Nash equilibria and optimal strategies for mean field games and stochastic control problems, respectively. Practically, I study optimal portfolio liquidation problems, utility maximisation, systemic risk and investigate the mathematical properties and financial background behind them. Here is a sample of my results: (1) We established the existence result for the liquidation games with strict liquidation constraint for the very first time. We studied a singular FBSDE system to characterize the Nash equilibrium. We found the optimal strategy for each trader was not as monotone as the one in the single player model. Indeed, the trader may sell out her assets shortly and buy back gradually, in order to avoid the negative drift generated by the interaction among all players. (2) We studied a general class of mean field games with singular controls by purely probabilistic approaches. To establish the existence result, we incorporated the Skorokhod M1 topology, which is rarely used in literature but proved to be essential in our problem. (3) We studied a portfolio game in the complete market with random returns and stochastic volatilities. The utility equilibrium was characterized by a new quadratic BSDE system. Qualification PhD (HU Berlin) ORCID ID 0000-0001-6965-0130