Research

My research is focused on Mathematical Finance and Applied Probability. It in particular involves the areas of stochastic analysis, stochastic control, optimal stopping, and the theory of viscosity solutions to fully nonlinear PDEs.

Working Papers  

   • Martingale Optimal Transport for General Measurable Claims
(with Arash Fahim)

First draft in preparation
   • Optimal Consumption in the Stochastic Ramsey Problem without Boundedness Constraints
(with Saeed Khalili)

Submitted [arXiv]
   • On Multi-Hypothesis Byzantine Sequential Change Detection
(with Shih-Chun Lin and Yu-Chih Huang)

Submitted [pdf]
   • Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time
(with Zhou Zhou)

Submitted [arXiv] [slides]
   • Stopping Behaviors of Naive and Non-Committed Sophisticated Agents when They Distort Probability
(with Adrien Nguyen-Huu and Xunyu Zhou)

Submitted [arXiv] [SSRN]
   • Optimal Equilibrium for Time-Inconsistent Stopping Problems -- the Discrete-Time Case
(with Zhou Zhou)

Submitted [arXiv]
   • Healthcare and Consumption with Aging
(with Paolo Guasoni)

Submitted [SSRN] [slides]

Publications

   • Time-Consistent Stopping under Decreasing Impatience
(with Adrien Nguyen-Huu)
Finance and Stochastics, 22 (2018), No. 1, pp 69-95.

[arXiv] [slides]
   • The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations
(with Xiaoshen Chen, Qingshuo Song, and Chao Zhu)
Journal of Mathematical Analysis and Applications, 451 (2017), No. 1, pp 448-472.

[arXiv] [slides]
   • Model-Independent Superhedging under Portfolio Constraints
(with Arash Fahim)
Finance and Stochastics, 20 (2016), No. 1, pp. 51-81.

[arXiv] [slides]
    On Hedging American Options under Model Uncertainty
(with Erhan Bayraktar and Zhou Zhou) 
SIAM Journal on Financial Mathematics6 (2015), No.1, pp. 425-447.

[arXiv]  
    Robust Maximization of Asymptotic Growth under Covariance Uncertainty
(with Erhan Bayraktar)
Annals of Applied Probability, 23 (2013), No. 5, pp. 1817-1840.

[arXiv] [audio & slides] [poster] 
    On the Multi-Dimensional Controller-and-Stopper Games
(with Erhan Bayraktar)
SIAM Journal on Control and Optimization, 51 (2013), No. 2, pp. 1263-1297.
 
[arXiv] [slides] 
    Outperforming the Market Portfolio with a Given Probability
(with Erhan Bayraktar and Qingshuo Song)
Annals of Applied Probability, 22 (2012), No. 4, pp. 1465-1494.

[arXiv] [slides]