Baeho Kim (Korea University): Conditional Tail Sampling for General Marked Point Processes

Baeho Kim (Korea University): Conditional Tail Sampling for General Marked Point Processes 

Joint work with Alex Shkolnik

Abstract: This study develops a simple but innovative simulation technique that can be employed in simulating a broad range of marked point processes, conditional on a tail event of interest. Our proposed conditional tail sampling algorithm guarantees that every simulated path hits the tail event with probability one, leading to an efficient estimation of tail probabilities and expected random quantities under the condition of rare events. By transforming the arrival times into uniformly distributed random variables, the simulation process becomes more streamlined and can significantly reduce the simulation variance under the limit of conditional probability measures associated with the specific tail event. Numerical results demonstrate the superior performance of the proposed approach in generating unbiased estimators for rare event probabilities of clustered epidemiological events in a network, calculating conditional expectations of the maximum drawdown for insurance risk analysis, and accurately determining fair credit spreads of risky fixed-income securities on (ultra-)short horizons under realistic yet complex model specifications.