Department of Mathematics

We review the advances in mathematical formulation of continuous-time principle-agent problem in the recent decade and provide a template for writing agency problems in a rigorous fashion. We present ... More

In stochastic control applications, typically only an ideal model (controlled transition kernel) is

assumed and the control design is based on the given model, raising the problem of performanc... More

We derive the short-maturity asymptotics for VIX option prices in local-stochastic volatility models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviati... More

We propose a continuous-time online estimator derived from a likelihood-based formulation for stochastic differential equations. The estimator admits a compact stochastic differential representation a... More

Regime-driven models are popular for addressing temporal patterns in both financial market performance and underlying stylized factors, wherein a regime describes periods with relatively homogeneous b... More

This dissertation develops a unified theoretical and algorithmic framework for the long-only mini-

mum variance (LOMV) portfolio problem under a one-factor covariance structure. The work begins... More