2期

最新文章

• Special Issue: On the interface between optimization and probability PREFACE AI翻译
  作者：Kovacevic, Raimund; Wets, Roger J-B; Wozabal, David
  作者单位：Technische Universitat Wien; University of California System; University of California Davis; Technical University of Munich
• Randomness and permutations in coordinate descent methods AI翻译
  作者：Gurbuzbalaban, Mert; Ozdaglar, Asuman; Vanli, Nuri Denizcan; Wright, Stephen J.
  作者单位：Rutgers University System; Rutgers University New Brunswick; Massachusetts Institute of Technology (MIT); University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
  摘要：We consider coordinate descent (CD) methods with exact line search on convex quadratic problems. Our main focus is to study the performance of the CD method that use random permutations in each epoch and compare it to the performance of the CD methods that use deterministic orders and random sampling with replacement. We focus on a class of convex quadratic problems with a diagonally dominant Hessian matrix, for which we show that using random permutations instead of random with-replacement sa...
• Risk forms: representation, disintegration, and application to partially observable two-stage systems AI翻译
  作者：Dentcheva, Darinka; Ruszczynski, Andrzej
  作者单位：Stevens Institute of Technology; Rutgers University System; Rutgers University New Brunswick
  摘要：We introduce the concept of a risk form, which is a real functional of two arguments: a measurable function on a Polish space and a measure on that space. We generalize the duality theory and the Kusuoka representation to this setting. For a risk form acting on a product of Polish spaces, we define marginal and conditional forms and we prove a disintegration formula, which represents a risk form as a composition of its marginal and conditional forms. We apply the proposed approach to two-stage...
• Martingale characterizations of risk-averse stochastic optimization problems AI翻译
  作者：Pichler, Alois; Schlotter, Ruben
  作者单位：Technische Universitat Chemnitz
  摘要：This paper addresses risk awareness of stochastic optimization problems. Nested risk measures appear naturally in this context, as they allow beneficial reformulations for algorithmic treatments. The reformulations presented extend usual dynamic equations by involving risk awareness in the problem formulation. Nested risk measures are built on risk measures, which originate by conditioning on the history of a stochastic process. We derive martingale properties of these risk measures and use th...
• Minimizing buffered probability of exceedance by progressive hedging AI翻译
  作者：Rockafellar, R. Tyrrell; Uryasev, Stan
  作者单位：University of Washington; University of Washington Seattle; State University System of Florida; University of Florida
  摘要：Stochastic programming problems have for a long time been posed in terms of minimizing the expected value of a random variable influenced by decision variables, but alternative objectives can also be considered, such as minimizing a measure of risk. Here something different is introduced: minimizing the buffered probability of exceedance for a specified loss threshold. The buffered version of the traditional concept of probability of exceedance has recently been developed with many attractive ...
• Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk AI翻译
  作者：van Beesten, E. Ruben; Romeijnders, Ward
  作者单位：University of Groningen
  摘要：In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total varia...
• Solving Lagrangian variational inequalities with applications to stochastic programming AI翻译
  作者：Rockafellar, R. Tyrrell; Sun, Jie
  作者单位：University of Washington; University of Washington Seattle; Curtin University
  摘要：Lagrangian variational inequalities feature both primal and dual elements in expressing first-order conditions for optimality in a wide variety of settings where multipliers in a very general sense need to be brought in. Their stochastic version relates to problems of stochastic programming and covers not only classical formats with inequality constraints but also composite models with nonsmooth objectives. The progressive hedging algorithm, as a means of solving stochastic programming problem...
• Theoretical and empirical analysis of trading activity AI翻译
  作者：Pohl, Mathias; Ristig, Alexander; Schachermayer, Walter; Tangpi, Ludovic
  作者单位：University of Vienna; University of Vienna; Princeton University
  摘要：Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of tradesN, the traded volumeV, the asset priceP, the squared volatility sigma 2 the bid-ask spreadSand the cost of tradingC. Different reasonings result in simple proportionality relations (scaling laws) between these variables. A basic proportionality is established betwe...
• Quantile-based risk sharing with heterogeneous beliefs AI翻译
  作者：Embrechts, Paul; Liu, Haiyan; Mao, Tiantian; Wang, Ruodu
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Geneva; Michigan State University; Michigan State University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Waterloo
  摘要：We study risk sharing problems with quantile-based risk measures and heterogeneous beliefs, motivated by the use of internal models in finance and insurance. Explicit forms of Pareto-optimal allocations and competitive equilibria are obtained by solving various optimization problems. For Expected Shortfall (ES) agents, Pareto-optimal allocations are shown to be equivalent to equilibrium allocations, and the equilibrium pricing measure is unique. For Value-at-Risk (VaR) agents or mixed VaR and ...
• Distributionally robust optimization with polynomial densities: theory, models and algorithms AI翻译
  作者：de Klerk, Etienne; Kuhn, Daniel; Postek, Krzysztof
  作者单位：Tilburg University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
  摘要：In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a knownambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distributions that give nature too much freedom to inflict damage. We thus introduce a new class of ambiguity sets that cont...