Related papers: Robust Stochastic Outperformance under Kullback-Le…
We provide optimal lower and upper bounds for the augmented Kullback-Leibler divergence in terms of the augmented total variation distance between two probability measures defined on two Euclidean spaces having different dimensions. We call…
This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber…
Navigation in complex and noisy environments is a key issue in diverse fields from biology to engineering. Despite extensive progress in numerical optimization methods for computing navigation policies, insights into how disorder reshapes…
A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific…
The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost…
We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $\gamma$ is optimal if and only if…
We prove that optimal traffic plans for the mailing problem in $\mathbb{R}^d$ are stable with respect to variations of the given coupling, above the critical exponent $\alpha=1-1/d$, thus solving an open problem stated in the book "Optimal…
Distributionally robust optimization tackles out-of-sample issues like overfitting and distribution shifts by adopting an adversarial approach over a range of possible data distributions, known as the ambiguity set. To balance conservatism…
We study the problem of nonnegative rank-one approximation of a nonnegative tensor, and show that the globally optimal solution that minimizes the generalized Kullback-Leibler divergence can be efficiently obtained, i.e., it is not NP-hard.…
This paper studies an $\alpha$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market…
We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…
In this paper we consider an optimal investment and reinsurance problem with partially unknown model parameters which are allowed to be learned. The model includes multiple business lines and dependence between them. The aim is to maximize…
The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative…
This paper studies a robust utility maximization problem for intractable claims under distributional ambiguity, where the distribution of the claim cannot be inferred from market information and its dependence with tradable assets is…
We consider a stochastic transportation problem between two prescribed probability distributions (a source and a target) over processes with general drift dependence and with free end times. First, and in order to establish a dual…
A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…
The aim of this paper is to compare the performances of the optimal strategy under parameters mis-specification and of a technical analysis trading strategy. The setting we consider is that of a stochastic asset price model where the trend…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
We study a problem of utility maximization under model uncertainty with information including jumps. We prove first that the value process of the robust stochastic control problem is described by the solution of a quadratic-exponential…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…