Related papers: Multilevel Path Branching for Digital Options
Rendering algorithms typically integrate light paths over path space. However, integrating over this one unified space is not necessarily the most efficient approach, and we show that partitioning path space and integrating each of these…
We present a novel technique of Monte Carlo error reduction that finds direct application in option pricing and Greeks estimation. The method is applicable to any LSV modelling framework and concerns a broad class of payoffs, including…
We propose a novel estimation framework for path-dependent functionals of Levy processes from discretely observed data. Traditional approaches rely on Monte Carlo simulation of full paths, which requires complete model specification and…
This work combines multilevel Monte Carlo (MLMC) with importance sampling to estimate rare-event quantities that can be expressed as the expectation of a Lipschitz observable of the solution to a broad class of McKean--Vlasov stochastic…
This work investigates the computational burden of pricing binary options in rare event regimes and introduces an adaptation of the adaptive multilevel splitting (AMS) method for financial derivatives. Standard Monte Carlo becomes…
We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options. Asian options are derivative contracts in which the underlying variable…
Designing efficient learning algorithms with complexity guarantees for Markov decision processes (MDPs) with large or continuous state and action spaces remains a fundamental challenge. We address this challenge for entropy-regularized MDPs…
We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level…
Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential…
Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…
Stochastic PDE eigenvalue problems often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In this paper we present an efficient multilevel quasi-Monte…
In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard…
We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation.…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…