Related papers: Leave-one-out least squares Monte Carlo algorithm …
Over the course of the past decade, a variety of randomized algorithms have been proposed for computing approximate least-squares (LS) solutions in large-scale settings. A longstanding practical issue is that, for any given input, the user…
Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer…
This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual…
Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with…
Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language…
In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to…
Penalized least squares methods are commonly used for simultaneous estimation and variable selection in high-dimensional linear models. In this paper we compare several prevailing methods including the lasso, nonnegative garrote, and SCAD…
In this work, we propose two low-complexity set-membership normalized least-mean-square (LCSM-NLMS1 and LCSM-NLMS2) algorithms to exploit the sparsity of an unknown system. For this purpose, in the LCSM-NLMS1 algorithm, we employ a function…
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…
I develop an algorithm to produce the piecewise quadratic that computes leave-one-out cross-validation for the lasso as a function of its hyperparameter. The algorithm can be used to find exact hyperparameters that optimize leave-one-out…
This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the…
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…
It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…
The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a…
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…
The least-mean-squares (LMS) algorithm is the most popular algorithm in adaptive filtering. Several variable step-size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance…
In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman (1997) to price a $\pi$-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of…
The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value.…
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…
A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the…