Related papers: Parallelizing Computation of Expected Values in Re…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
This paper develops three polynomial-time pricing techniques for European Asian options with provably small errors, where the stock prices follow binomial trees or trees of higher-degree. The first technique is the first known Monte Carlo…
We developed a replica exchange method that is effectively parallelizable even if the computational cost of the Monte Carlo moves in the parallel replicas are considerably different, for instance, because the replicas run on different type…
Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…
Monte Carlo Tree Search is a cornerstone algorithm for online planning, and its root-parallel variant is widely used when wall clock time is limited but best performance is desired. In environments with continuous action spaces, how to best…
The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and…
Monte Carlo Tree Search (MCTS) is a widely used approach for policy improvement through search with increasing popularity for real world applications. Due to the sequential and deterministic nature of its search, runtime-scaling of MCTS…
The real options approach is now considered an effective alternative to the corporate DCF model for a feasibility study. The current paper offers a practical methodology employing binomial trees and real options techniques for evaluating…
In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
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…
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…
The Multi-Commodity Pickup and Delivery Vehicle Routing Problem aims to optimize the pickup and delivery of multiple unique commodities using a fleet of several agents with limited payload capacities. This paper addresses the challenge of…
Random-expiry options are nontraditional derivative contracts that may expire early based on a random event. We develop a methodology for pricing these options using a trinomial tree, where the middle path is interpreted as early expiry. We…
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…
A sorted set (or map) is one of the most used data types in computer science. In addition to standard set operations, like Insert, Remove, and Contains, it can provide set-set operations such as Union,Intersection, and Difference. Each of…