Lectures by Professor Guangwu Liu of City University of Hong Kong
time: 2022-05-24

TitleGreen Nested Simulation with Application in Portfolio Risk Measurement

SpeakerProfessor Guangwu Liu

Time: Thursday ,May  26 , 2022, PM:3:00-4:00

Dress: Conference room 4131, building 4 

Inviter:  Prof.Zhijian He       


AbstractNested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates scenarios and the inner-level simulations are ran in each outer scenario to estimate the corresponding conditional expectation. The resulting sample of conditional expectations is then used to estimate different risk measures of interest. Despite its flexibility, nested simulation is notorious for its heavy computational burden.

We introduce a novel simulation procedure that reuses inner simulation outputs to improve the efficiency and accuracy in solving nested estimation problems. We analyze the convergence rates of the bias, variance, and MSE of the resulting estimator. In addition, central limit theorems and variance estimators are presented, which lead to asymptotically valid confidence intervals for the nested risk measure of interest. Numerical studies on two financial risk measurement problems show consistent results with the asymptotic analysis and show that the proposed approach outperforms the standard nested simulation and a state-of-art regression approach for nested estimation problems.