Turnpike Property and Convergence Rate for an Investment Model with General Utility Functions

In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.Comment: 29 page

Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems

In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.Comment: 18 page

Doc2EDAG: An End-to-End Document-level Framework for Chinese Financial Event Extraction

Most existing event extraction (EE) methods merely extract event arguments within the sentence scope. However, such sentence-level EE methods struggle to handle soaring amounts of documents from emerging applications, such as finance, legislation, health, etc., where event arguments always scatter across different sentences, and even multiple such event mentions frequently co-exist in the same document. To address these challenges, we propose a novel end-to-end model, Doc2EDAG, which can generate an entity-based directed acyclic graph to fulfill the document-level EE (DEE) effectively. Moreover, we reformalize a DEE task with the no-trigger-words design to ease the document-level event labeling. To demonstrate the effectiveness of Doc2EDAG, we build a large-scale real-world dataset consisting of Chinese financial announcements with the challenges mentioned above. Extensive experiments with comprehensive analyses illustrate the superiority of Doc2EDAG over state-of-the-art methods. Data and codes can be found at https://github.com/dolphin-zs/Doc2EDAG.Comment: Accepted by EMNLP 201

Realtime Profiling of Fine-Grained Air Quality Index Distribution using UAV Sensing

Given significant air pollution problems, air quality index (AQI) monitoring has recently received increasing attention. In this paper, we design a mobile AQI monitoring system boarded on unmanned-aerial-vehicles (UAVs), called ARMS, to efficiently build fine-grained AQI maps in realtime. Specifically, we first propose the Gaussian plume model on basis of the neural network (GPM-NN), to physically characterize the particle dispersion in the air. Based on GPM-NN, we propose a battery efficient and adaptive monitoring algorithm to monitor AQI at the selected locations and construct an accurate AQI map with the sensed data. The proposed adaptive monitoring algorithm is evaluated in two typical scenarios, a two-dimensional open space like a roadside park, and a three-dimensional space like a courtyard inside a building. Experimental results demonstrate that our system can provide higher prediction accuracy of AQI with GPM-NN than other existing models, while greatly reducing the power consumption with the adaptive monitoring algorithm

Content adaptive sparse illumination for Fourier ptychography

Fourier Ptychography (FP) is a recently proposed technique for large field of view and high resolution imaging. Specifically, FP captures a set of low resolution images under angularly varying illuminations and stitches them together in Fourier domain. One of FP's main disadvantages is its long capturing process due to the requisite large number of incident illumination angles. In this letter, utilizing the sparsity of natural images in Fourier domain, we propose a highly efficient method termed as AFP, which applies content adaptive sparse illumination for Fourier ptychography by capturing the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework with both simulations and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP by around 30%-60%