Related papers: Optimal Risk Sharing Without Preference Convexity:…
We study a general allocation setting where agent valuations are concave additive. In this model, a collection of items must be uniquely distributed among a set of agents, where each agent-item pair has a specified utility. The objective is…
This note is devoted to the distributed optimization problem of multi-agent systems with nonconvex velocity constraints, nonuniform position constraints and nonuniform stepsizes. Two distributed constrained algorithms with nonconvex…
In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for single-integrator and double-integrator multi-agent systems. Two distributed adaptive optimization algorithm is…
A monopolist wishes to maximize her profits by finding an optimal price policy. After she announces a menu of products and prices, each agent $x$ will choose to buy that product $y(x)$ which maximizes his own utility, if positive. The…
We consider a persuasion problem between a sender and a receiver whose utility may be nonlinear in her belief; we call such receivers risk-conscious. Such utility models arise when the receiver exhibits systematic biases away from…
This work develops effective distributed strategies for the solution of constrained multi-agent stochastic optimization problems with coupled parameters across the agents. In this formulation, each agent is influenced by only a subset of…
We study the principal-agent problem. We show that $b$-convexity of the space of products, a condition which appears in a recent paper by Figalli, Kim and McCann \cite{fkm}, is necessary to formulate the problem as a maximization over a…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which multiple risk-averse agents choose their decisions in such a way to minimize their individual accumulated…
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces…
In this paper, we provide extended convolution bounds for the Fr\'{e}chet problem and discuss related implications in quantitative risk management. First, we establish a new form of inequality for the Range-Value-at-Risk (RVaR). Based on…
We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk…
In this paper, we consider the nonconvex minimization problem of the value-at-risk (VaR) that arises from financial risk analysis. By considering this problem as a special linear program with linear complementarity constraints (a bilevel…
The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…
We study distributed optimization in a cooperative multi-agent setting, where agents have to agree on the usage of shared resources and can communicate via a time-varying network to this purpose. Each agent has its own decision variables…
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it…
We study efficient risk sharing among risk-averse agents in an economy with a large, finite number of states. Following a random shock to an initial agreement, agents may renegotiate. If they require a minimal utility improvement to accept…
We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…
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…