Optimal execution strategies in limit order books with general shape functions

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type

RAVEN: a GUI and an Artificial Intelligence Engine in a Dynamic PRA Framework

Increases in computational power and pressure for more accurate simulations and estimations of accident scenario consequences are driving the need for Dynamic Probabilistic Risk Assessment (PRA) [1] of very complex models. While more sophisticated algorithms and computational power address the back end of this challenge, the front end is still handled by engineers that need to extract meaningful information from the large amount of data and build these complex models. Compounding this problem is the difficulty in knowledge transfer and retention, and the increasing speed of software development. The above-described issues would have negatively impacted deployment of the new high fidelity plant simulator RELAP-7 (Reactor Excursion and Leak Analysis Program) at Idaho National Laboratory. Therefore, RAVEN that was initially focused to be the plant controller for RELAP-7 will help mitigate future RELAP-7 software engineering risks. In order to accomplish such a task Reactor Analysis and V

Drift dependence of optimal trade execution strategies under transient price impact

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting

Intrawell stochastic resonance versus interwell stochastic resonance in underdamped bistable systems

We show that, for periodically driven noisy underdamped bistable systems, an intrawell stochastic resonance can exist, together with the conventional interwell stochastic resonance, resulting in a double maximum in the power spectral amplitude at the forcing frequency as a function of the noise intensity. The locations of the maxima correspond to matchings of deterministic and stochastic time scales in the system. In this paper we present experimental evidence of these phenomena and a phemonological nonadiabatic description in terms of a noise-controlled nonlinear dynamic resonance

Dynamic PRA: an Overview of New Algorithms to Generate, Analyze and Visualize Data

State of the art PRA methods, i.e. Dynamic PRA (DPRA) methodologies, largely employ system simulator codes to accurately model system dynamics. Typically, these system simulator codes (e.g., RELAP5 ) are coupled with other codes (e.g., ADAPT, RAVEN that monitor and control the simulation. The latter codes, in particular, introduce both deterministic (e.g., system control logic, operating procedures) and stochastic (e.g., component failures, variable uncertainties) elements into the simulation. A typical DPRA analysis is performed by: 1. Sampling values of a set of parameters from the uncertainty space of interest 2. Simulating the system behavior for that specific set of parameter values 3. Analyzing the set of simulation runs 4. Visualizing the correlations between parameter values and simulation outcome Step 1 is typically performed by randomly sampling from a given distribution (i.e., Monte-Carlo) or selecting such parameter values as inputs from the user (i.e., Dynamic Event Tre

Proper orthogonal decomposition of solar photospheric motions

The spatio-temporal dynamics of the solar photosphere is studied by performing a Proper Orthogonal Decomposition (POD) of line of sight velocity fields computed from high resolution data coming from the MDI/SOHO instrument. Using this technique, we are able to identify and characterize the different dynamical regimes acting in the system. Low frequency oscillations, with frequencies in the range 20-130 microHz, dominate the most energetic POD modes (excluding solar rotation), and are characterized by spatial patterns with typical scales of about 3 Mm. Patterns with larger typical scales of 10 Mm, are associated to p-modes oscillations at frequencies of about 3000 microHz.Comment: 8 figures in jpg in press on PR

Planilhas de cálculo para estimativa do ciclo de culturas, a partir de graus-dia.

A temperatura é um dos principais fatores de controle do desenvolvimento vegetal. Por volta de 1735, Reaumur, na França, realizou os primeiros estudos relacionando desenvolvimento vegetal e temperatura do ar, quando ele observou que o somatório da temperatura do ar era praticamente constante durante o ciclo de desenvolvimento de várias espécies em diferentes anos (Pereira et ai., 2002). Dessa forma, foi desenvolvido o conceito de Graus-dia que baseia-se no fato de que existem duas temperaturas base, uma mínima e outra máxima, entre as quais a planta tem pleno desenvolvimento. Fora desse intervalo, a planta não se desenvolve ou o faz em taxas muito reduzidas (Pereira et al., 2002). Nesse sentido, a temperatura pode ser considerada o fator principal de controle do desenvolvimento das plantas e de grande influência na sua distribuição geográfica (Holmes e Robertson, 1959). Assim, pode-se considerar que a teoria dos graus-dia pode ser utilizada, na estimativa dos ciclos das culturas, previsão de data de colheita e, principalmente, no zoneamento agrícola, fazendo com que este último deixe de ser estático e passe a ser dinâmico. Pedro Júnior et al. (1975) mostraram que o cálculo de graus-dia a partir de equações de regressão múltipla, para o estado de São Paulo, é viável, tornando-se uma técnica útil para o planejamento do plantio e colheita. A partir dessas afirmações, este trabalho teve como objetivo desenvolver uma planilha de cálculo em ambiente computacional Excel for WindowsTM para facilitar os cálculos de graus-dia a partir da estimativa das temperaturas médias de várias regiões e auxiliar no cálculo dos ciclos das culturas.CBAgro 2005

An Optimal Execution Problem with Market Impact

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of the optimal strategies change completely, depending on the amount of the trader's security holdings and where optimal strategies in the Black-Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal execution problem with market impact" in Finance and Stochastics (2014

Planilhas de cálculo para estimativa do ciclo de culturas, a partir de graus-dia.

Foram criadas duas planilhas de cálculo de graus-dia a partir da diferença entre a temperatura média do ar e a temperatura base da cultura. A primeira planilha faz cálculos mensais e a temperatura é estimada a partir de equações de regressão propostas para vários Estados brasileiros. Assim, pode ser usada para planejamento de plantio, colheita e zoneamento agrícola das culturas. A segunda, faz cálculos diários com dados inseridos manualmente e, portanto, tem mais flexibilidade para inserção de fórmulas. Foram realizados testes para se verificar a aplicabilidade das planilhas, comparando-se os resultados obtidos pelas planilhas com dados obtidos em experimentos de campo. Também foram realizados testes de suas aplicações no zoneamento agrícola. Todas se mostraram de grande utilidade para o planejamento e o zoneamento