Mitigating the effect of tail risk has gained prominence in a variety of applications where safety is of paramount importance. Tail risk averseness is typically incorporated into standard optimisation models by penalising decisions which lead to poor tail performance, often captured through the use of measures such as Value at Risk (V@R) and Conditional Value at Risk (CV@R). Operationalising these risk sensitive optimisation problems however, requires accurate computation of tail expectations of random variables and may incur a large sample requirement. In this talk, we discuss the use of Black Box Importance Sampling (BBIS) to mitigate this difficulty. Specifically, we show that given black box access to the loss causing covariates, BBIS significantly reduces the sample complexity of solving a wide range of tail risk averse optimisation problems. This differs from most of the state of the art, where algorithms to reduce sample requirements are carefully tuned to the problem at hand. The distribution/loss agnostic nature of BBIS leads to a wide applicability, ranging from relatively simple instances such as linear portfolio optimisation to complicated ones such as two stage problems. Numerical simulations support our theoretical claims and help establish the utility of BBIS in a number of practically relevant settings.
This talk is based on a number of joint works with Karthyek Murthy, SUTD. I will not assume any prerequisites beyond a basic understanding of probability. Technicalities will be kept to the minimum, and the exposition will be mostly pictorial.