Important Sampling Of Different States With Optimal-path Based On Large-deviations

Efficient simulation of rare events has been an active research area in applied probability. Rare events arise in many applications including telecommunications, computer and communication networks, insurance and finance. There are many different methods of rare events simulation, such as importance sampling, conditional Monte Carlo, cross-entropy, large-deviations approach and splitting.In this paper, we consider one of efficient simulations of rare events in light-tailed settings. It relies on the combination between large-deviations and importance sampling. Firstly, we get the optimal path by using the large-deviations approach. Secondly, owe to the interplay between large deviations techniques and importance sampling, we can calculate the exponential change of measure corresponding to the optimal path. Finally, we choose one of importance sampling algorithms about different states. In the paper, we set up two examples in SAS by using the method, including the one about the sum of light-tailed and a complex digital barrier options.