Related papers: A fast Monte Carlo scheme for additive processes a…
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…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at $m$ fixed dates. Our approach yields unbiased estimators with standard deviation $O(\epsilon)$ in $O(m + (1/\epsilon)^{2})$ expected…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
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…
An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
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…
Process monitoring and control requires detection of structural changes in a data stream in real time. This article introduces an efficient sequential Monte Carlo algorithm designed for learning unknown changepoints in continuous time. The…
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
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…
As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges. As it is known, the…
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…
Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…
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…