-
作者：Xing, Jie; Ma, Jingtang; Zheng, Harry
作者单位：Guizhou University of Finance & Economics; Southwestern University of Finance & Economics - China; Imperial College London
摘要：In this paper, we study a finite horizon optimal investment stopping problem with an unobservable random variable for the return of a risky asset. Using the Bayesian filter and the dual control approach, we transform the original primal problem into a dual finite horizon optimal stopping problem, which results in the dual value function satisfying a variational inequality with two state variables. For a class of utility functions that includes power utility and non-hyperbolic absolute risk ave...
-
作者：Boros, Endre; Lee, Joonhee
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick; Pace University
摘要：Hailperin (1965) introduced a linear programming formulation to a difficult family of problems, originally proposed by Boole (1854, 1868). Hailperin's model is computationally still difficult and involves an exponential number of variables (in terms of a typical input size for Boole's problem). Numerous papers provided efficiently computable bounds for the minimum and maximum values of Hailperin's model by using aggregation that is a monotone linear mapping to a lower dimensional space. In man...
-
作者：Goodwin, Ariel; Lewis, Adrian S.; Lopez-Acedo, Genaro; Nicolae, Adriana
作者单位：Cornell University; Cornell University; University of Sevilla; Babes Bolyai University from Cluj
摘要：The classical Euclidean subgradient algorithm extends, via tangent constructions and exponential maps, to geodesically convex optimization on manifolds. General complexity analysis for manifolds with an upper curvature bound of zero, as developed by Zhang and Sra in 2016 [Zhang H, Sra S (2016) First-order methods for geodesically convex optimization. Feldman V, Rakhlin A, Shamir O, eds. Proc. 29th Conf. Learn. Theory, vol. 49 (PMLR, New York), 1617-1638] depends unavoidably on an additional lo...
-
作者：Hafalir, Isa E.; Kojima, Fuhito; Yenmez, M. Bumin; Yokote, Koji
作者单位：University of Technology Sydney; University of Tokyo; Washington University (WUSTL); Durham University; Ozyegin University; Aoyama Gakuin University
摘要：We provide optimal solutions to an institution that has distributional objectives when choosing from a set of applications based on merit (or priority). For example, in college admissions, administrators may want to admit a diverse class in addition to choosing students with the highest qualifications. We provide a family of choice rules that maximize merit subject to attaining a level of the distributional objective. We study the desirable properties of choice rules in this family and use the...
-
作者：Luner, Alan; Grimmer, Benjamin
作者单位：Johns Hopkins University
摘要：This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather than reporting the final iterate, one can report either a convex combination of the iterates (averaging) or a generic combination of the iterates (extrapolation). For several common stepsize sequences, including recently developed accelerated periodically long stepsize schemes, we show averaging cannot improve gradien...
-
作者：Han, Xia; Wang, Qiuqi; Wang, Ruodu; Xia, Jianming
作者单位：Nankai University; Nankai University; University System of Georgia; Georgia State University; University of Waterloo; Chinese Academy of Sciences
摘要：In the literature on risk measures, cash subadditivity was proposed to replace cash additivity, motivated by the presence of stochastic or ambiguous interest rates and defaultable contingent claims. Cash subadditivity has been traditionally studied together with quasi-convexity, in a way similar to cash additivity with convexity. In this paper, we study cash-subadditive risk measures without quasi-convexity. One of our major results is that a general cash-subadditive risk measure can be repres...
-
作者：Xia, Li; Ma, Shuai
作者单位：Sun Yat Sen University
摘要：Dynamic optimization of mean and variance in Markov decision processes (MDPs) is a long-standing challenge caused by the failure of dynamic programming. In this paper, we propose a new approach to finding the globally optimal policy for combined metrics of steady-state mean and variance in an infinite-horizon undiscounted MDP. By introducing the concepts of pseudo mean and pseudo variance, we convert the original problem to a bilevel MDP problem, where the inner one is a standard MDP optimizin...
-
作者：Li, Guoyin; Mordukhovich, Boris; Zhu, Jiangxing
作者单位：University of New South Wales Sydney; Wayne State University; Yunnan University
摘要：This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our primary focus is on examining this concept concerning first-order and second-order stationary points. We develop an extended convergence framework that enables us to derive superlinear and quadratic convergence under the generalized metric subregularity con...
-
作者：Portales, Leo; Cazelles, Elsa; Pauwelsc, Edouard
作者单位：Communaute d'universites et etablissements de Toulouse (Comue); Universite de Toulouse (EPE); Universite Toulouse 1 Capitole; Institut National Polytechnique de Toulouse; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Communaute d'universites et etablissements de Toulouse (Comue); Communaute d'universites et etablissements de Toulouse (Comue); Universite Toulouse 1 Capitole; Toulouse School of Economics
摘要：Lloyd's algorithm is an iterative method that solves the quantization problem, that is, the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as a gradient method on a certain quantization functional which is given by optimal transport. We study the sequential convergence (to a single accumulation point) for two variants of Lloyd's method: (i) optimal quantization with an arbitrary discrete measu...
-
作者：Li, Bo; Pang, Guodong
作者单位：Nankai University; Nankai University; Rice University
摘要：We study single-server queues with Hawkes arrivals whose intensity process depends on the queue length through the self-exciting function, and with independent and identically distributed general service times, under the first-come first-served discipline. We prove the functional law of large numbers and functional central limit theorems (FCLT) for the joint processes of the arrivals, queue-length, and workload processes, in the heavy traffic regime. The fluid limit is given by a set of nonlin...
