Related papers: Pricing Bermudan options using nonparametric regre…

We propose a new `hedged' Monte-Carlo (HMC) method to price financial derivatives, which allows to determine simultaneously the optimal hedge. The inclusion of the optimal hedging strategy allows one to reduce the financial risk associated…

In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…

This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by…

In this paper, we investigate optimal stopping problems in a continuous-time framework where only a discrete set of stopping dates is admissible, corresponding to the Bermudan option, within the so-called exploratory formulation. We…

Suppose $\mu$ and $\nu$ are probability measures on $\mathbb R$ satisfying $\mu \leq_{cx} \nu$. Let $a$ and $b$ be convex functions on $\mathbb R$ with $a \geq b \geq 0$. We are interested in finding \[ \sup_{\mathcal M} \sup_{\tau}…

It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…

The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…

Local variable selection aims to test for the effect of covariates on an outcome within specific regions. We outline a challenge that arises in the presence of non-linear effects and model misspecification. Specifically, for common…

Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient…

We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly…

In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…

Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to…

Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…

The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…

A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…

The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions…

We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…

Selective prediction, where a model has the option to abstain from making a decision, is crucial for machine learning applications in which mistakes are costly. In this work, we focus on distributional regression and introduce a framework…

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…

We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a…