Related papers: Distributionally Robust Inference for Extreme Valu…

We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic…

We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and…

This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…

In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…

We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…

In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random…

We propose a spectral clustering algorithm for analyzing the dependence structure of multivariate extremes. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure…

We consider a one-dimensional diffusion which solves a stochastic differential equation with Borel-measurable coefficients in an open interval. We allow for the endpoints to be inaccessible or absorbing. Given a Borel-measurable function…

This paper formulates algorithms to upper-bound the maximum Value-at-Risk (VaR) of a state function along trajectories of stochastic processes. The VaR is upper bounded by two methods: minimax tail-bounds (Cantelli/Vysochanskij-Petunin) and…

There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…

This paper investigates the impact of distributional uncertainty on key risk measures under the partial knowledge of underlying distributions characterized by their first two moments and shape information (specifically symmetry and/or…

In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state…

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the…

We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…

We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…

Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…

Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to maximize the expected…