Optimal Execution with Dynamic Order Flow Imbalance

We examine optimal execution models that take into account both market microstructure impact and informational costs. Informational footprint is related to order flow and is represented by the trader's influence on the flow imbalance process, while microstructure influence is captured by instantaneous price impact. We propose a continuous-time stochastic control problem that balances between these two costs. Incorporating order flow imbalance leads to the consideration of the current market state and specifically whether one's orders lean with or against the prevailing order flow, key components often ignored by execution models in the literature. In particular, to react to changing order flow, we endogenize the trading horizon $T$. After developing the general indefinite-horizon formulation, we investigate several tractable approximations that sequentially optimize over price impact and over $T$. These approximations, especially a dynamic version based on receding horizon control, are shown to be very accurate and connect to the prevailing Almgren-Chriss framework. We also discuss features of empirical order flow and links between our model and "Optimal Execution Horizon" by Easley et al (Mathematical Finance, 2013).Comment: 31 pages, 8 figure

Mathematical Literacy: The Effects of Mathematics Journals on Student Understanding of Fractions in a Montessori Classroom

It is a typical Monday morning. As students enter the classroom wearing brightly colored polo shirts embroidered with the school logo, their smiles are equally bright. This Title I public school in the heart of the city where 96% of the students qualify for free or reduced lunch has recently opened a Montessori option. Walking into the classroom, one 5th grade student eagerly asks, “Who’s on the bread committee this week?” Baking bread is a weekly occurrence in the upper elementary (4th – 6th grade) Montessori classroom. During the first week of school, this same student vehemently threw materials to the floor declaring, “I HATE fractions!” In an effort to positively engage students in mathematics, the weekly bread-making tradition was implemented. Through cooking, students experience the importance of fractions in everyday life. Each week, two students work together, read several recipes, select one, and submit a precise written list of needed ingredients. The next day, with the aid of a bread machine bought for $10 at the local thrift store, the students work together to follow directions, read fractions, measure ingredients, and bake bread. Once baked, students divide the bread into equal portions and serve. After several months of this routine, some recipes will need to be doubled or halved, and on it goes… The bread committee provides a “hook” for some resistant students. It is also a practical application of the role of literacy in mathematics. The choice to focus on mathematical literacy and the effect of journaling on student understanding was influenced by research around mathematical vocabulary as well as the instructional practices of noted educators and researchers. The rigor of upper elementary math as defined in the common core requires students to not only perform calculations with accuracy, but to demonstrate strong reading comprehension through the interpretation of real-world word problems, and to articulate an understanding of MATHEMATICAL LITERACY 3 mathematical reasoning through clear and concise writing. Achieving grade level proficiency has practical life implications for students because research showed mathematical knowledge during elementary school as a strong predictor of financial stability in adulthood, and understanding fractions in fifth grade as a predictor of overall achievement in mathematics (Siegler & Lortie-Forgues, 2015)

Lebesgue constant for the Strömberg wavelet

AbstractLet S denote the Strömberg wavelet in L2(R) and Ps,n(s∈Z,n∈Z∪{∞}), the orthogonal projection onto the space spanned by the functions 2r/2S(2rt−m), where r⩽s, m<n+1 (i.e. Ps,n are partial sums for the orthonormal wavelet basis generated by S). We show that the maximum of the norms of the extensions of the operators Ps,n onto L∞(R) is equal to 2+(2−3)2

Automatic Transcription of Northern Prinmi Oral Art: Approaches and Challenges to Automatic Speech Recognition for Language Documentation

One significant issue facing language documentation efforts is the transcription bottleneck: each documented recording must be transcribed and annotated, and these tasks are extremely labor intensive (Ćavar et al., 2016). Researchers have sought to accelerate these tasks with partial automation via forced alignment, natural language processing, and automatic speech recognition (ASR) (Neubig et al., 2020). Neural network—especially transformer-based—approaches have enabled large advances in ASR over the last decade. Models like XLSR-53 promise improved performance on under-resourced languages by leveraging massive data sets from many different languages (Conneau et al., 2020). This project extends these efforts to a novel context, applying XLSR-53 to Northern Prinmi, a Tibeto-Burman Qiangic language spoken in Southwest China (Daudey & Pincuo, 2020). Specifically, this thesis aims to answer two questions. First, is the XLSR-53 ASR model useful for first-pass transcription of oral art recordings from Northern Prinmi, an under-resourced tonal language? Second, does preprocessing target transcripts to combine grapheme clusters—multi-character representations of lexical tones and characters with modifying diacritics—into more phonologically salient units improve the model\u27s predictions? Results indicate that—with substantial adaptations—XLSR-53 will be useful for this task, and that preprocessing to combine grapheme clusters does improve model performance

Looking Beyond the Immediate Crisis Response: Analyzing the Organizational Culture to Understand the Crisis

This article analyzes the organizational culture at Olivet College in Michigan. The organizational response has been the subject of the most of the discussion on organizational exigencies. Perhaps most telling is the focus on organizational planning and preparation. Crisis planning allows individuals within the organization to change their view of the factors that constitute a crisis, since planning often reduces the severity of the event by lowering the uncertainties of how to respond. Communication is central to the resolution of a crisis situation. In fact, some would argue that organizations should focus on crisis communication instead of crisis management