Journal ArticleDOI
Adaptative Monte Carlo Method, A Variance Reduction Technique
Reads0
Chats0
TLDR
An adaptative variance reduction method for Monte Carlo simulations that uses importance sampling scheme based on a change of drift and develops two applications of the procedure for variance reduction in a Monte Carlo computation in finance and in reliability.Abstract:
In this article we propose an adaptative variance reduction method for Monte Carlo simulations. The method uses importance sampling scheme based on a change of drift. The change of drift is selected adaptatively through the Monte Carlo computation by using a suitable sequence of approximation. We state and prove theoretical results supporting the use of the method. We develop two applications of the procedure for variance reduction in a Monte Carlo computation in finance and in reliability.read more
Citations
More filters
Journal ArticleDOI
Minimum variance importance sampling via Population Monte Carlo
TL;DR: In this article, a mixture of importance functions, called a D-kernel, can be iteratively optimized to achieve the minimum asymptotic variance for a function of interest among all possible mixtures.
Journal ArticleDOI
Computing VaR and CVaR using Stochastic Approximation and Adaptive Unconstrained Importance Sampling
TL;DR: A first Robbins–Monro (RM) procedure based on Rockafellar–Uryasev's identity for the CVaR and it is proved that the weak convergence rate of the resulting procedure is ruled by a Central Limit Theorem with minimal variance and its efficiency is illustrated on several typical energy portfolios.
Journal ArticleDOI
Unconstrained Recursive Importance Sampling
Vincent Lemaire,Gilles Pagès +1 more
TL;DR: In this paper, an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for Monte Carlo simulations is proposed. But this method does not consider the regularity of the density of the law without assume smoothness of the payoff.
Posted Content
Adaptive optimal allocation in stratified sampling methods
Pierre Etore,Benjamin Jourdain +1 more
TL;DR: In this article, a stratified sampling algorithm is proposed in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum.
Journal ArticleDOI
Unconstrained recursive importance sampling
Vincent Lemaire,Gilles Pagès +1 more
TL;DR: In this paper, an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for Monte Carlo simulations is proposed. But this method does not consider the regularity of the density of the law without assume smoothness of the payoff.
References
More filters
Journal ArticleDOI
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Book
Stochastic approximation and recursive algorithms and applications
Harold J. Kushner,George Yin +1 more
TL;DR: A review of continuous time models can be found in this paper, where the authors present an algorithm for the Ergodic Cost Problem: Formulation and Algorithms 7.1 Formulation of the control problem 7.2 A Jacobi Type Iteration 7.3 Approximation in Policy Space 7.4 Numerical Methods 7.5 The Control Problem 7.6 The Interpolated Process 7.7 Computations 7.8 Linear Programming 7.
Book
Introduction to stochastic calculus applied to finance
Damien Lamberton,Bernard Lapeyre +1 more
TL;DR: The Black-Scholes model as mentioned in this paper is a discrete-time formalism for estimating martingales and arbitrage opportunities in the stock market with continuous-time processes, and it has been applied to American options.
Book
Random iterative models
Marie Duflo,Stephen S. Wilson +1 more
TL;DR: This book provides a wide-angle view of stochastic approximation, linear and non-linear models, controlled Markov chains, estimation and adaptive control, learning, and algorithms with good performances and reasonably easy computation.