Related papers: Reinforced optimal control
In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each…
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to…
A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least…
We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the…
We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations,…
We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We develop two Regression Monte Carlo algorithms (value and performance iteration) to solve general problems of optimal stochastic control of discrete-time Markov processes. We formulate our method within an innovative framework that allow…
Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model with the integrand as response and the control…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
The multi-level Monte Carlo method proposed by M. Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper, a modified…
The optimal stopping problem is a category of decision problems with a specific constrained configuration. It is relevant to various real-world applications such as finance and management. To solve the optimal stopping problem,…
I develop a numerical algorithm for stochastic impulse control in the spirit of Regression Monte Carlo for optimal stopping. The approach consists in generating statistical surrogates (aka functional approximators) for the continuation…
Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…