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作者：Horst, Ulrich; Paulsen, Michael
作者单位：Humboldt University of Berlin
摘要：We define a stochastic model of a two-sided limit order book in terms of its key quantities best bid [ask] price and the standing buy [sell] volume density. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a limit theorem. The limit theorem states that, given regularity conditions on the random order flow, the key quantities converge in probability to a tractable continuous limiting model. In the lim...
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作者：Yamazaki, Kazutoshi
作者单位：Kansai University
摘要：A new approach to solve the continuous-time stochastic inventory problem using the fluctuation theory of Levy processes is developed. This approach involves the recent developments of the scale function that is capable of expressing many fluctuation identities of spectrally one-sided Levy processes. For the case with a fixed cost and a general spectrally positive Levy demand process, we show the optimality of an (s,S)-policy. The optimal policy and the value function are concisely expressed vi...
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作者：Herings, P. Jean-Jacques; Predtetchinski, Arkadi
作者单位：Maastricht University
摘要：We consider n-player perfect information games with payoff functions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payoff functions. We show that there exists a best response cycle of length four, that is, a sequence of four pure strategy profiles where every successive element is a best response to the previous one. T...
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作者：O'Sullivan, Michael; Veinott, Arthur F., Jr.
作者单位：University of Auckland; Stanford University
摘要：This paper studies the problem of finding a stationary strong present-value optimal and, more generally, an n-present-value optimal, policy for an infinite-horizon stationary finite-state-action substochastic Markov decision chain. A policy is strong present-value optimal if it has maximum present value for all small positive interest rates rho. A policy is n-present-value optimal if its present value falls below the maximum present value for all small positive rho by O(rho(n+1)). The importan...
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作者：Engau, Alexander
作者单位：Children's Hospital Colorado; University of Colorado System; University of Colorado Anschutz Medical Campus; University of Colorado Denver
摘要：The mathematical equivalence between linear scalarizations in multiobjective programming and expected- value functions in stochastic optimization suggests to investigate and establish further conceptual analogies between these two areas. In this paper, we focus on the notion of proper efficiency that allows us to provide a first comprehensive analysis of solution and scenario tradeoffs in stochastic optimization. In generalization of two standard characterizations of properly efficient solutio...
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作者：Renault, Jerome; Venel, Xavier
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Paris School of Economics
摘要：We study long-term Markov Decision Processes and Gambling Houses, with applications to any partial observation MDPs with finitely many states and zero-sum repeated games with an informed controller. We consider a decision-maker which is maximizing the weighted sum Sigma(t >= 1) theta(t)r(t), where rt is the expected reward of the t-th stage. We prove the existence of a very strong notion of long-term value called general uniform value, representing the fact that the decision-maker can play wel...
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作者：He, Bingsheng; Tao, Min; Yuan, Xiaoming
作者单位：Southern University of Science & Technology; Nanjing University; Hong Kong Baptist University
摘要：Recently, in He et al. [He BS, Tao M, Yuan XM (2012) Alternating direction method with Gaussian back substitution for separable convex programming. SIAM J. Optim. 22(2):313-340], we have showed the first possibility of combining the Douglas-Rachford alternating direction method of multipliers (ADMM) with a Gaussian back substitution procedure for solving a convex minimization model with a general separable structure. This paper is a further study on this theme. We first derive a general algori...
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作者：Subramanian, Ajay; Yang, Baozhong
作者单位：University System of Georgia; Georgia State University; University System of Georgia; Georgia State University
摘要：We analyze a continuous-time stochastic control problem that arises in the study of several important issues in financial economics. An agent controls the drift and volatility of a diffusion output process by dynamically selecting one of an arbitrary (but finite) number of projects and the termination time. The optimal policy depends on the projects' risk-adjusted drifts that are determined by their drifts, volatilities, and the curvature (or relative risk aversion) of the agent's payoff funct...
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作者：Keskin, N. Bora; Zeevi, Assaf
作者单位：Duke University; Columbia University
摘要：We consider a dynamic pricing problem in which a seller faces an unknown demand model that can change over time. The amount of change over a time horizon of T periods is measured using a variation metric that allows for a broad spectrum of temporal behavior. Given a finite variation budget, we first derive a lower bound on the expected performance gap between any pricing policy and a clairvoyant who knows a priori the temporal evolution of the underlying demand model, and then we design famili...
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作者：Queyranne, Maurice; Tardella, Fabio
作者单位：University of British Columbia; Universite Catholique Louvain; Sapienza University Rome
摘要：The Caratheodory, Helly, and Radon numbers are three main invariants in convexity theory. These invariants have been determined, exactly or approximately, for a number of different convexity structures. We consider convexity structures defined by the sublattices and by the convex sublattices of finite-dimensional Euclidian, integer, and Boolean spaces. Such sublattices arise in submodular optimization (lattice programming) and in monotone comparative statics of optimization and fixed point pro...
