Related papers: Shape-constrained Estimation of Value Functions

We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure…

We study the estimation of the value function for continuous-time Markov diffusion processes using a single, discretely observed ergodic trajectory. Our work provides non-asymptotic statistical guarantees for the least-squares…

We derive an asymptotic theory of nonparametric estimation for a time series regression model $Z_t=f(X_t)+W_t$, where \ensuremath\{X_t\} and \ensuremath\{Z_t\} are observed nonstationary processes and $\{W_t\}$ is an unobserved stationary…

We use the geometry of suitably generalised potentials to solve risk-sensitive Markovian optimal stopping problems. As in the linear case due to Dynkin and Yushkievich (1967), the value function is the pointwise infimum of those functions…

In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…

In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A…

We develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has…

We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…

We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…

Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…

We propose a new non parametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove…

We construct an unbiased estimator for function value evaluated at the solution of a partial differential equation with random coefficients. We show that the variance and expected computational cost of our estimator are finite and our…

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

We present a new unbiased algorithm that estimates the expected value of f(U) via Monte Carlo simulation, where U is a vector of d independent random variables, and f is a function of d variables. We assume that f does not depend equally on…

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…

We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…

We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…