Research Interests

Simulation analytics is a new simulation output analysis paradigm that views simulations as a controlled way of generating and collecting data, after which predictive analytics methods can be applied. Simulation analytics takes advantages of the flexibility in simulation modeling of complex systems, its ability to generate large amount of data, and the trending development of novel data science tools. This line of research aims to develop novel simulation analytics methods: (1) Utilizes some problem structures such as tail risk estimation to circumvent (hopefully many) inner simulations by efficiently identify tail scenarios, where a given simulation budget will then be concentrated. (2) Utilizes novel supervised and unsupervised learning methods such as Gaussian process modeling and clustering improve the overall efficiency of computationally demanding simulation experiments.

Nested simulation is a popular tool for risk management of large portfolios of financial and insurance products. It is, however, notoriously known for its heavy computational burden; sometimes prohibitively so. In some cases, such as tail risk estimation, only the simulation outputs in the tail scenarios affect the accuracy of the risk estimator; majority of the simulation outputs are under-utilized for finding the ranks of estimates in different scenarios. Using known data analytics methods, such as proxy modeling, we are able to identify tail scenarios with minimal computation, then concentrate a given simulation budget to the importance tail scenarios. We provide theoretical support and intuition for such importance allocated nested simulation (IANS) procedure.

Given a large portfolio of financial and actuarial products, valuing every product using simulation is extremely time-consuming. Viewing simulation as a data generator, however, can take advantages of existing data analytics methods. For instance, unsupervised learning such a clustering can be used to identify a few key representative products in the portfolio. After valuing these representative products via simulation, supervised learning methods such as Gaussian process modeling can be calibrated to learn the simulation model's input-output relationship. Such calibrated model can be used to efficiently valuate every product in the portfolio. Such compressor-simulator-predictor procedure is shown to be highly efficient and effective.

Green simulation is a novel simulation design paradigm that aims to reuse and recycle simulation outputs to enhance the accuracy and computational efficiency of simulation experiments. We propose to view simulation experiments as computational investments that not only benefit the current but also the future decision-making processes. Our research aims to develop efficient methods of output recycling and to examine their theoretical properties and practical performances.

In many financial and actuarial applications, simulation models are often run repeatedly to perform the same task, e.g., derivative pricing with slightly different inputs, e.g., newly observed market information. In these cases, the simulation outputs from previous experiments are informative of the current experiment. Reusing previous simulation outputs, rather than the common practice of disgarding them, can greatly increase the simulation efficiency for the current and all future tasks.

Metamodeling is a useful tool for understanding the input-output relationship in complex black-box simulation models. The exploration vs. exploitation tradeoff is a central problem in the simulation design for different metamodeling techniques. Some green simulation methods, such as green simulation via likelihood ratio, can be viewed as unbiased metamodels. By cataloging these methods, we discover metamodels that are both unbiased and have low variance and also identify new metamodels that have not been studied before.

For instance, bootstrap-based input uncertainty quantification and risk estimation for dynamic hedging programs. In a typical nested simulation procedure, estimation for each outer scenario uses only the inner simulations associated with that scenario. We propose pooling inner simulations from all outer scenarios to estimate for every scenario. Such pooling of inner simulation greatly improves accuracy, reducing computations, or both.

Financial entities around the globe are interconnected and this giant global financial network requires sophisticated systemic risk management. This research addresses the question of risk attribution, “Who contributed how much risk to the network's overall systemic risk?”, which is a key question in systemic risk management. Seven risk attribution methods are developed to suit different systemic risk management objectives in different time and scale.