相关论文: Why does Monte Carlo fail to work properly in high…

We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…

By precisely writing down the matrix element of the local Boltzmann operator, we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With current formula, the…

Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…

This is a response to the comment by J. Lidmar on our work in Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622. We show explicitly that, contrary to the statements in the comment, our scaling analysis correctly reproduces the Josephson…

The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and…

We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates…

Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by…

Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…

We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss…

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…

The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given…

A recent reformulation [1] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a…

We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in…

In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized…

We study the $L_1$-approximation of $d$-variate monotone functions based on information from $n$ function evaluations. It is known that this problem suffers from the curse of dimensionality in the deterministic setting, that is, the number…

Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In…

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…

We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…