Nested simulation for estimating portfolio losses within a time horizon

We consider the problem of estimating the probability that a stochastic process observed at discrete time intervals exceeds a specified threshold. We further assume that the value of this process at any time, along any realization, is a conditional expectation which is not known analytically but can be estimated via simulation. This leads to a nested simulation procedure. One application of this arises in risk management where our interest may be in the probability that a portfolio exceeds a threshold of losses at specified times. Here, if the portfolio consists of sophisticated derivatives, then as a function of the underlying security prices, the portfolio value at any time is a conditional expectation that may be evaluated via simulation. In our analysis, we note that conditional on the outer loop of simulation, our estimation problem is related to the large deviations based ordinal optimization framework, so that similar analysis may be used to efficiently allocate computational budget in portfolio evaluations at different times. We also propose a resource allocation methodology based on statistical hypothesis testing.