Related papers: Optimal importance sampling for L\'evy Processes
Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested…
In this paper, we implement and test two types of market-based models for European-type options, based on the tangent Levy models proposed recently by R. Carmona and S. Nadtochiy. As a result, we obtain a method for generating Monte Carlo…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
In this article, we present an approach which allows to take into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associeted options. Specifically, the marginal distribution of…
Multi-sample, importance-weighted variational autoencoders (IWAE) give tighter bounds and more accurate uncertainty estimates than variational autoencoders (VAE) trained with a standard single-sample objective. However, IWAEs scale poorly:…
Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte…
We propose an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for Monte Carlo simulations. We consider different parametric families based on the Girsanov theorem and…
Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
The expected value of information (EVI) is the most powerful measure of sensitivity to uncertainty in a decision model: it measures the potential of information to improve the decision, and hence measures the expected value of outcome.…
Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the…
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for L\'evy-driven SDEs or their integrands for stochastic integrals. Main results are bordered…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic…
We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of…
Efficiently pricing multi-asset options is a challenging problem in quantitative finance. When the characteristic function is available, Fourier-based methods are competitive compared to alternative techniques because the integrand in the…
We study Monte Carlo estimation of the expected value of sample information (EVSI) which measures the expected benefit of gaining additional information for decision making under uncertainty. EVSI is defined as a nested expectation in which…
This article is devoted to the design of importance sampling method for the Monte Carlo simulation of a linear transport equation. This model is of great importance in the simulation of inertial confinement fusion experiments. Our method is…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…