Related papers: A General Duality Relation with Applications in Qu…

The quantification of diversification benefits due to risk aggregation plays a prominent role in the (regulatory) capital management of large firms within the financial industry. However, the complexity of today's risk landscape makes a…

It is known that the set of perturbed data is key in robust optimization (RO) modelling. Distributionally robust optimization (DRO) is a methodology used for optimization problems affected by random parameters with uncertain probability…

The necessity to deal with uncertain data is a major challenge in decision making. Robust optimization emerged as one of the predominant paradigms to produce solutions that hedge against uncertainty. In order to obtain an even more…

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an…

The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a…

We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is…

The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…

This paper focuses on optimizing probabilities of events of interest defined over general controlled discrete-time Markov processes. It is shown that the optimization over a wide class of $\omega$-regular properties can be reduced to the…

A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this…

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is…

We consider the problem of distributionally robust multimodal machine learning. Existing approaches often rely on merging modalities on the feature level (early fusion) or heuristic uncertainty modeling, which downplays modality-aware…

In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…

Despite remarkable success in a variety of applications, it is well-known that deep learning can fail catastrophically when presented with out-of-distribution data. Toward addressing this challenge, we consider the domain generalization…

Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…

In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization…

In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the…

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…