Chao Zhou
Email Address
matzc@nus.edu.sg
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Publication Lifetime Ruin Problem Under High-watermark Fees and Drift Uncertainty(2019-09-03) Lee, Junbeom; Yu, Xiang; Zhou, Chao; Dr Zhou Chao; MATHEMATICSThis paper aims to make a new contribution to the study of lifetime ruin problem by considering investment in two hedge funds with high-watermark fees and drift uncertainty. Due to multi-dimensional performance fees that are charged whenever each fund profit exceeds its historical maximum, the value function is expected to be multi-dimensional. New mathematical challenges arise as the standard dimension reduction cannot be applied, and the convexity of the value function and Isaacs condition may not hold in our ruin probability minimization problem with drift uncertainty. We propose to employ the stochastic Perron's method to characterize the value function as the unique viscosity solution to the associated Hamilton Jacobi Bellman (HJB) equation without resorting to the proof of dynamic programming principle. The required comparison principle is also established in our setting to close the loop of stochastic Perron's method.Publication Portfolio liquidation under factor uncertainty(2019-09-04) Horst, Ulrich; Xia, Xiaonyu; Zhou, Chao; Dr Zhou Chao; MATHEMATICS; RISK MANAGEMENT INSTITUTEWe study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also establish an asymptotic analysis of the robust model for small amount of uncertainty and analyse the effect of robustness on optimal trading strategies and liquidation costs. In particular, in our model ambiguity aversion is observationally equivalent to increased risk aversion. This suggests that ambiguity aversion increases liquidation rates.Publication Horizon-unbiased Investment with Ambiguity(2019-04) Lin, Qian; Sun, Xianming; Zhou, Chao; Dr Zhou Chao; MATHEMATICSIn the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process, reflecting an investor's dynamic preference. We show that the market risk premium and the utility risk premium jointly determine the investors' trading direction and the worst-case scenarios of the risky asset's mean return and volatility. The closed-form formulas for the optimal investment strategies are given in the special settings of the CRRA preference.Publication Mean Field Exponential Utility Game: A Probabilistic Approach(2020) FU GUANXING; Su, Xizhi; ZHOU CHAO; Dr Zhou Chao; MATHEMATICSWe study an $N$-player and a mean field exponential utility game. Each player manages two stocks; one is driven by an individual shock and the other is driven by a common shock. Moreover, each player is concerned not only with her own terminal wealth but also with the relative performance of her competitors. We use the probabilistic approach to study these two games. We show the unique equilibrium of the $N$-player game and the mean field game can be characterized by a novel multi-dimensional FBSDE with quadratic growth and a novel mean-field FBSDEs, respectively. The well-posedness result and the convergence result are established.