Stochastic simulation provides a powerful analytics method for the prediction and uncertainty quantification in complex stochastic systems, and is especially useful for rare event analytics where events happen with extremely small probabilities but have large severity. Rare event analytics are crucial in areas such as financial engineering and aviation safety analysis.
We consider the question of efficient estimation in the tails of Gaussian copulas defined by a set of constraints. The central idea is to identify certain dominatingpoint(s) of the feasible set, and appropriately shift and scale an exponential distribution for subsequent use within an importance sampling measure. >>Download Nagaraj, K., J. Xu, S. Ghosh, and R. Pasupathy. Efficient Estimation in the Tails of Gaussian Copulas. Under review for Operations Research.
We proposed an importance sampling method for the NORTA sampling procedure with an application for Conditional Value-at-Risk (CVaR) estimation (the proposed method was patented in 2013).
>>Download Huang, P., D. Subramanian, J. Xu. 2010. An importance sampling method for portfolio CVaR estimation with Gaussian copula models. Proceedings of 2010 Winter Simulation Conference, IEEE, Piscataway, NJ, 2790-2800.
Adaptive nested rare event simulation
Nested simulation algorithms are used in several scientific investigations such as climate, statistical mechanics, and financial and actuarial risk management. Recently, these methods have also been used in the context of Bayesian computations and are referred to as Nested Sampling. In several of these problems, the inner level computation typically involves simulating events with very small probability, leading to rare event importance sampling methods. The quality of the resulting estimates depend on the allocation of computational resources between inner and outer level simulations. We introduce a novel adaptive rare event simulation algorithm that allocates the computational resources by taking in to account marginal changes in the rare event probabilities. We establish the consistency and efficiency of our algorithm and theoretically and numerically compare our results with the non-adaptive methods. We illustrate the proposed methods with several examples. >>Download "Adaptive Nested Rare Event Simulation Algorithms"
Rare Event Simulation for Stochastic Fixed Point Equations Related to the Smoothing Transformation
In several applications arising in compute science, cascade theory, and other applied areas, it is of interest to evaluate the tail probabilities of non-homogeneous stochastic fixed point equations. Recently, techniques have been developed for the related linear recursions, yielding tail estimates and importance sampling methods for these recursions. However, such methods do not routinely generalize to non-homogeneous recursions. Drawing on techniques from the weighted branching process literature, we present a consistent, strongly efficient importance sampling algorithm for estimating the tail probabilities for the case of nonhomogeneous recursions. >>Download "Rare Event Simulation for Stochastic Fixed Point Equations Related to the Smoothing Transformation"