Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(Xε(t)) : ε > 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let Ψε(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X(t)) as ε → 0. As a consequence, we give exact asymptotics for log Ψ...

The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic particle filter (i.e., importance sampling using the prior as the importance density) does not work i...

The valuation of basket default swaps depends crucially on the joint default probability of the underlying assets in the basket. It is known that this probability can be modeled by means of a copula function which links the marginal default probabilities to a joint probability. The valuation bears risk due to the uncertainty of the copula, the relation of the assets to each other and the margin...

M Carlo simulation is widely used to measure the credit risk in portfolios of loans, corporate bonds, and other instruments subject to possible default. The accurate measurement of credit risk is often a rare-event simulation problem because default probabilities are low for highly rated obligors and because risk management is particularly concerned with rare but significant losses resulting fr...

Full likelihood inference under Kingman’s coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) method have been applied successfully. Both methods can be expressed in terms of families of intractable conditional sampling distributions (CSDs), and rely on principled approximations for accurate inference. Recently,...

We extend a previously developed method, based on Wagner’s stochastic formulation of importance sampling, to the calculation of reaction rates and to a simple quantitative description of finite-temperature, average dynamic paths. Only the initial and final states are required as input—no information on transition state~s! is necessary. We demonstrate the method for a single particle moving on t...

The paper introduces a family of approximate schemes that extend the process of computing sample mean in importance sampling from the conventional OR space to the AND/OR search space for graphical models. All the sample means are defined on the same set of samples and trade time with variance. At one end is the AND/OR sample tree mean which has the same time complexity as the conventional OR sa...

Microfacet models have proven very successful for modeling light reflection from rough surfaces. In this paper we review microfacet theory and demonstrate how it can be extended to simulate transmission through rough surfaces such as etched glass. We compare the resulting transmission model to measured data from several real surfaces and discuss appropriate choices for the microfacet distributi...

We present a technique to efficiently importance sample distant, all-frequency illumination in indoor scenes. Standard environment sampling is inefficient in such cases since the distant lighting is typically only visible through small openings (e.g. windows). This visibility is often addressed by manually placing a portal around each window to direct samples towards the openings; however, unif...

We consider the problem of off-policy policy selection in reinforcement learning: using historical data generated from running one policy to compare two or more policies. We show that approaches based on importance sampling can be unfair—they can select the worse of two policies more often than not. We give two examples where the unfairness of importance sampling could be practically concerning...