In recent two decades, long-horizon regression has become a popular choice for testing mean reversion in stock prices. Due to overlapping and multi-period return summation, finite sample analysis of long-horizon regression coefficient is complicated and largely unavailable in the literature. Empirical studies almost entirely rely on asymptotic tests, which can have serious size distortions and ...

In this paper, we develop a finite horizon model predictive control algorithm which is robust to modelling uncertainties. A moving average system matrix is constructed to capture modelling uncertainties and facilitate the future output prediction. The paper is mainly focused on the step tracking problem. Using linear matrix inequality techniques, the design is converted into a semi-definite opt...

In [1], we have demonstrated that robust optimization of linear finite-horizon control in a discrete time linear dynamical system affected by uncertain disturbances becomes computationally tractable if, rather than using natural parameterization of a linear output-based control law, one passes to a specific re-parameterization of the law, representing it as affine control law based on the so ca...

We study multilateral bargaining games where agents disagree over their bar-gaining power. We show that if agents are extremely optimistic, there may be costlydelays in an arbitrarily long finite game but if optimism is moderate, all sufficientlylong games end in immediate agreement. We show that the game with extremeoptimism is highly unstable in the finite-horizon, and we exam...

This paper presents properties of a control law which quantizes the unconstrained solution to a unitary horizon quadratic programme. This naı̈ve quantized control law underlies many popular algorithms, such as -converters and decision feedback equalities, and is easily shown to be globally optimal for horizon one. However, the question arises as to whether it is also globally optimal for horizon...

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in ge...

In the real time formulation of finite temperature field theories, one introduces an additional set of fields (type-2 fields) associated to each field in the original theory (type-1 field). In [1], in the context of the AdS-CFT correspondence, Maldacena interpreted type-2 fields as living on a boundary behind the black hole horizon. However, below the Hawking-Page transition temperature, the th...

For a given initial state, a constrained infinite horizon linear quadratic optimal control problem can be reduced to a finite dimensional problem [12]. To find a conservative estimate of the size of the reduced problem, the existing algorithms require the on-line solutions of quadratic programs [10] or a linear program [2]. In this paper, we first show based on the Lyapunov theorem that the clo...

We study optimal taxation when consumers have temptation and self-control problems. Embedding the class of preferences developed by Gul and Pesendorfer into a standard macroeconomic setting, we first prove, in a two-period model, that the optimal policy is to subsidize savings when consumers are tempted by “excessive” impatience. The savings subsidy improves welfare because it makes succumbing ...

Energy Harvesting (EH) has emerged as a promising technique for Green Communications and it is a novel technique to prolong the lifetime of the wireless networks with replenishable nodes. In this paper, we consider the energy shortage analysis of fixed rate transmission in communication systems with energy harvesting nodes. First, we study the finite-horizon transmission and provide the general...