We present a generic non-nested Monte Carlo procedure for computing true upper bounds for Bermudan products, given an approximation of the Snell envelope. The pleonastic “true” stresses that, by construction, the estimator is biased above the Snell envelope. The key idea is a regression estimator for the Doob martingale part of the approximative Snell envelope, which preserves the martingale pr...

The waste-recycling Monte Carlo (WRMC) algorithm introduced by physicists is a modification of the (multi-proposal) Metropolis–Hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard (multi-proposal) Metropolis–Hastings algorithm uses only the accepted proposals. In this paper we extend the WRMC algorithm to a general control variate technique and ex...

Consider a semi-Markov process that, after entering state /, next goes to state j with probability P/ y , and given that the next state isy, the time until the transition from / to j occurs is a random variable with distribution F/j having mean m(i,j). Starting in state 0, suppose we are interested in estimating n = E[T], where T, called the cover time, is the time until all of the states 1,2,....

Asian options are of particular importance for commodity products which have low trading volumes (e.g. crude oil), since price manipulation is inhibited. Hence, the pricing of such options becomes one of the most interesting fields. Since there are no known closed form analytical solutions to arithmetic average Asian options, many numerical methods are applied. This paper deals with pricing of ...

We consider situations in Bayesian analysis where we have a family of priors νh on the parameter θ, where h varies continuously over a space H, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function f of θ. How do we efficiently estimate the posterior expectation of f(θ) simultaneously for all h in H? The second problem...

The well-known variance reduction methods—the method of importance sampling and the method of control variates—can be exploited if an approximation of the required solution is known. Here we employ conditional probabilistic representations of solutions together with the regression method to obtain sufficiently inexpensive (although rather rough) estimates of the solution and its derivatives by ...

Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al., 2016; Maddison et al., 2016) has taken a different approach, introducing a continuous relaxation of discrete variables to produce low-variance, but biased, gra...

We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties related to their initial spatial arrangement. The resulting 2000-dimensional space is sampled using a non-intrusive and computationally efficient Multi-Level Mon...

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not all integrals are in closed form, whi...

We synergistically apply queueing theory, integer programming, and stochastic simulation to determine an optimal staffing policy for a repair call handling center. A stationary Markovian queueing model is employed to determine minimal staffing levels for a sequence of time intervals with varying call volumes and mean handling times. These staffing requirements populate an integer programmodel f...