Radio Frequency Identification (RFID)

Abstract. We present a framework for obtaining fully polynomial time approximation schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely, the calculus of K-approximation functions and the calculus of K-approximation sets. Using our framework, we provide the first FPTASs for several NP-hard problems in various fields of research such as knapsack models, logistics, operations management, economics, and mathematical finance. Extensions of our framework via the use of the newly established computational rules are also discussed.Key words. fully polynomial time approximation schemes, stochastic dynamic programming, K-approximation AMS subject classifications. 68Q25, 68W25, 90B05, 90B06, 90C15, 90C39, 90C40, 90C56, 90C59

We develop a framework for obtaining (deterministic) Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. Using our framework, we give the first FPTASs for several NP-hard problems in various fields of research such as knapsack-related problems, logistics, operations management, economics, and mathematical finance. IntroductionDynamic Programming (DP). Dynamic Programming is an algorithmic technique used for solving sequential, or multi-stage, decision problems and is a fundamental tool in combinatorial optimization (e.g., [17], Section 2.5 in [3], and Chapter 8 in [30]). A discrete time finite time horizon dynamic program is to find an optimal policy over a finite time horizon that minimizes the average cost. At the beginning of a time period, the state of the system is observed and an action is taken. Based on exogenous stochastic information, the state, and the action, the system incurs a single-period cost and transitions into a new state. The goal is to find a policy that realizes the minimal total expected cost over the entire time horizon.We can formally model this by means of Bellman's optimality equation. Let z t (I t ) be the cost-to-go (also known as the value function). The value z t (I t ) is simply the cost of an optimal policy from time period t to the end of the time horizon, given that at the beginning of time period t the state is I t . The equation reads (1.1) z t (I t ) = min x t ∈A t (I t ) E Dt {g t (I t , x t , D t ) + z t+1 (f t (I t , x t , D t ))}.

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Deep neural networks (DNNs) are powerful types of artificial neural networks (ANNs) that use several hidden layers. They have recently gained considerable attention in the speech transcription and image recognition community (Krizhevsky et al., 2012) for their superior predictive properties including robustness to overfitting. However their application to algorithmic trading has not been previously researched, partly because of their computational complexity. This paper describes the application of DNNs to predicting financial market movement directions. In particular we describe the configuration and training approach and then demonstrate their application to backtesting a simple trading strategy over 43 different Commodity and FX future mid-prices at 5-minute intervals. All results in this paper are generated using a C++ implementation on the Intel Xeon Phi co-processor which is 11.4x faster than the serial version and a Python strategy backtesting environment both of which are available as open source code written by the authors.