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We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo…
This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed…
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is…
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
High statistical precision is critical for Monte Carlo (MC) samples in high energy physics and is degraded by negatively weighted events. This paper investigates a procedure to learn the relationship between the negative and positive weight…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has especially simple form for time discretised diffusion processes. We…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for…
The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of…
Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly…
It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…
Accept-reject based Markov chain Monte Carlo (MCMC) methods are the workhorse algorithm for Bayesian inference. These algorithms, like Metropolis-Hastings, require choosing a proposal distribution which is typically informed by the desired…
This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…
In this study, we explore the efficiency of the Monte Carlo Tree Search (MCTS), a prominent decision-making algorithm renowned for its effectiveness in complex decision environments, contingent upon the volume of simulations conducted.…
This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in…