Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs

This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both investment and consumption strategies, and model uncertainty on both drift and volatility. With the help of explicit solutions, we quantify the impacts of uncertain market parameters, portfolio-consumption constraints and borrowing costs on the optimal strategies and their time monotone properties.Comment: 35 pages, 8 tables, 1 figur

N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole

We construct four-dimensional N=4 super-Yang-Mills theories on a conic sphere with various background R-symmetry gauge fields. We study free energy and supersymmetric Renyi entropy using heat kernel method as well as localization technique. We find that the universal contribution to the partition function in the free field limit is the same as that in the strong coupling limit, which implies that it may be protected by supersymmetry. Based on the fact that, the conic sphere can be conformally mapped to $S^1\times H^3$ and the R-symmetry background fields can be supported by the R-charges of black hole, we propose that the holographic dual of these theories are five-dimensional, supersymmetric STU topological black holes. We demonstrate perfect agreement between N=4 super-Yang-Mills theories in the planar limit and the STU topological black holes.Comment: 1+48 pages, v2:typo fixed+references adde

Improvements on lower bounds for the blow-up time under local nonlinear Neumann conditions

This paper studies the heat equation $u_t=\Delta u$ in a bounded domain $\Omega\subset\mathbb{R}^{n}(n\geq 2)$ with positive initial data and a local nonlinear Neumann boundary condition: the normal derivative $\partial u/\partial n=u^{q}$ on partial boundary $\Gamma_1\subseteq \partial\Omega$ for some $q>1$, while $\partial u/\partial n=0$ on the other part. We investigate the lower bound of the blow-up time $T^{*}$ of $u$ in several aspects. First, $T^{*}$ is proved to be at least of order $(q-1)^{-1}$ as $q\rightarrow 1^{+}$. Since the existing upper bound is of order $(q-1)^{-1}$, this result is sharp. Secondly, if $\Omega$ is convex and $|\Gamma_{1}|$ denotes the surface area of $\Gamma_{1}$, then $T^{*}$ is shown to be at least of order $|\Gamma_{1}|^{-\frac{1}{n-1}}$ for $n\geq 3$ and $|\Gamma_{1}|^{-1}\big/\ln\big(|\Gamma_{1}|^{-1}\big)$ for $n=2$ as $|\Gamma_{1}|\rightarrow 0$, while the previous result is $|\Gamma_{1}|^{-\alpha}$ for any $\alpha<\frac{1}{n-1}$. Finally, we generalize the results for convex domains to the domains with only local convexity near $\Gamma_{1}$.Comment: 28 page

Selective Encoding for Abstractive Sentence Summarization

We propose a selective encoding model to extend the sequence-to-sequence framework for abstractive sentence summarization. It consists of a sentence encoder, a selective gate network, and an attention equipped decoder. The sentence encoder and decoder are built with recurrent neural networks. The selective gate network constructs a second level sentence representation by controlling the information flow from encoder to decoder. The second level representation is tailored for sentence summarization task, which leads to better performance. We evaluate our model on the English Gigaword, DUC 2004 and MSR abstractive sentence summarization datasets. The experimental results show that the proposed selective encoding model outperforms the state-of-the-art baseline models.Comment: 10 pages; To appear in ACL 201