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  

   • Epstein-Zin Utility Maximization on Random Horizons 
(with Joshua Aurand)

Submitted [arXiv]
   • Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time 
(with Zhou Zhou)

Submitted [arXiv[slides]

Publications

     Journal Articles

   • Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time
(with Zhou Zhou)
Mathematical Finance, forthcoming.

[arXiv] [slides]
   • General Stopping Behaviors of Naive and Non-Committed Sophisticated Agents, with Application to Probability Distortion
(with Adrien Nguyen-Huu and Xunyu Zhou)
Mathematical Finance, forthcoming.

[arXiv] [SSRN]
   • Consumption, Investment, and Healthcare with Aging
(with Paolo Guasoni)
Finance and Stochastics, 23 (2019), No. 2, pp 313-358.

[arXiv[SSRN] [slides]
   • Optimal Consumption in the Stochastic Ramsey Problem without Boundedness Constraints
(with Saeed Khalili)
SIAM Journal on Control and Optimization, 57 (2019), No. 2, pp 783-809.

[arXiv]
   • The Optimal Equilibrium for Time-Inconsistent Stopping Problems - the Discrete-Time Case
(with Zhou Zhou)
SIAM Journal on Control and Optimization, 57 (2019), No. 1, pp 590-609.

[arXiv]
   • 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] 
     Conference Articles

   • A Tight Converse to the Asymptotic Performance of Byzantine Distributed Sequential Change Detection
(with Shih-Chun Lin and Yu-Chih Huang)
IEEE International Symposium on Information Theory, forthcoming.

[pdf]
   • On Byzantine Distributed Sequential Change Detection with Multiple Hypotheses
(with Shih-Chun Lin and Yu-Chih Huang)
IEEE International Symposium on Information Theory, forthcoming.

[pdf]