Problem definition: Bargaining situations are ubiquitous in economics and management. We consider the problem of bargaining for a fair ex-ante distribution of random profits arising from a cooperative effort of a fixed set of risk-averse agents. Our approach integrates optimal managerial decision making into bargaining situations with random outcomes and explicitly models the impact of … Read more
In the absence of direct demand-side bids for certain reliability products in the wholesale electricity markets, Independent System Operators (ISOs) traditionally use fixed demand requirements with penalty factors to clear the market. This approach does not allow proper tradeoffs between reliability and cost due to the inelasticity of the fixed requirements. Therefore, ISOs have been … Read more
The scheduling of drilling and hydraulic fracturing of wells in an unconventional oil field plays an important role in the profitability of the field. A key challenge arising in this problem is the requirement that neither drilling nor oil production can be done at wells within a specified neighborhood of a well being fractured. We … Read more
We decompose the copositive cone $\copos{n}$ into a disjoint union of a finite number of open subsets $S_{\cal E}$ of algebraic sets $Z_{\cal E}$. Each set $S_{\cal E}$ consists of interiors of faces of $\copos{n}$. On each irreducible component of $Z_{\cal E}$ these faces generically have the same dimension. Each algebraic set $Z_{\cal E}$ is … Read more
We introduce a new class of distributionally robust optimization problems under decision dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the … Read more
This paper studies a Nash game arising in portfolio optimization. We introduce a new general multi-portfolio model and state sufficient conditions for the monotonicity of the underlying Nash game. This property allows us to treat the problem numerically and, for the case of nonunique equilibria, to solve hierarchical problems of equilibrium selection. We also give … Read more
We consider uncertain robust electricity market equilibrium problems including transmission and generation investments. Electricity market equilibrium modeling has a long tradition but is, in most of the cases, applied in a deterministic setting in which all data of the model are known. Whereas there exist some literature on stochastic equilibrium problems, the field of robust … Read more
We study a robust optimal control of discrete time Markov chains with finite terminal T and bounded costs using probability distortion. The time inconsistency of these operators and hence its lack of dynamic programming are discussed. Due to that, dynamic versions of these operators are introduced and its availability for dynamic programming are demonstrated. Based … Read more
Beginning in the 1960s, techniques from operations research began to be used to generate political districting plans. A classical example is the integer programming model of Hess et al. (Operations Research 13(6):998–1006, 1965). Due to the model’s compactness-seeking objective, it tends to generate contiguous or nearly-contiguous districts, although none of the model’s constraints explicitly impose … Read more
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we … Read more