Three-dimensional radiative transfer calculations on an SIMD machine applied to accretion disks

We have developed a tool to solve the radiative transfer equation for a three-dimensional astrophysical object on the SIMD computer MasPar MP-1. With this tool we can rapidly calculate the image of such an object as seen from an arbitrary direction and at an arbitrary wavelength. Such images and spectra can then be used to directly compare observations with the model. This tool can be applied to many different areas in astrophysics, e.g., HI disks of galaxies and polarized radiative transfer of accretion columns onto white dwarfs. Here we use this tool to calculate the image and spectrum of a simple model of an accretion disk

Explicit solution to an optimal switching problem in the two regimes case

24 pagesThis paper considers the problem of determining the optimal sequence of stopping times for a diffusion process subject to regime switching decisions. This is motivated in the economics literature, by the investment problem under uncertainty for a multi-activity firm involving opening and closing decisions. We use a viscosity solutions approach, and explicitly solve the problem in the two regimes case when the state process is of geometric Brownian nature

Numerical approximation for an impulse control problem arising in portfolio selection under liquidity risk

18 pagesWe investigate numerical aspects of a portfolio selection problem studied in [10], in which we suggest a model of liquidity risk and price impact and formulate the problem as an impulse control problem under state constraint. We show that our impulse control problem could be reduced to an iterative sequence of optimal stopping problems. Given the dimension of our problem and the complexity of its solvency region, we use Monte Carlo methods instead of finite difference methods to calculate the value function, the transaction and no-transaction regions. We provide a numerical approximation algorithm as well as numerical results for the optimal transaction strategy

Uncovering Market Disorder and Liquidity Trends Detection

The primary objective of this paper is to conceive and develop a new methodology to detect notable changes in liquidity within an order-driven market. We study a market liquidity model which allows us to dynamically quantify the level of liquidity of a traded asset using its limit order book data. The proposed metric holds potential for enhancing the aggressiveness of optimal execution algorithms, minimizing market impact and transaction costs, and serving as a reliable indicator of market liquidity for market makers. As part of our approach, we employ Marked Hawkes processes to model trades-through which constitute our liquidity proxy. Subsequently, our focus lies in accurately identifying the moment when a significant increase or decrease in its intensity takes place. We consider the minimax quickest detection problem of unobservable changes in the intensity of a doubly-stochastic Poisson process. The goal is to develop a stopping rule that minimizes the robust Lorden criterion, measured in terms of the number of events until detection, for both worst-case delay and false alarm constraint. We prove our procedure's optimality in the case of a Cox process with simultaneous jumps, while considering a finite time horizon. Finally, this novel approach is empirically validated by means of real market data analyses

Optimal dividend and capital structure with debt covenants

We consider an optimal dividend and capital structure problem for a firm which holds a certain amount of debt to which is associated a financial-ratio covenant between the creditors and the firm. We study optimal policies under a bankruptcy framework using a mixed reduced and structural approach in modelling default and liquidation times. Once in default, the firm is given a grace period during which it may inject more capital to correct the situation. The firm is liquidated if, by the end of the grace period, assets do not exceed the debt. Under this setup, we maximize the discounted amount of dividends distributed minus the capital injected up to the time of bankruptcy. It gives rise to a two-dimensional singular control problem leading to a non-standard system of variational inequalities. Beyond the usual viscosity characterization, we completely solve this problem and obtain a description of the continuation, dividend and capital injection regions enabling us to fully characterize the optimal policies. We conclude the paper with numerical results and illustrations

A mixed singular/switching control problem for a dividend policy with reversible technology investment

We consider a mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular control. We prove that our mixed problem can be decoupled in two pure optimal stopping and singular control problems. Furthermore, we describe the form of the optimal strategy by means of viscosity solution techniques and smooth-fit properties on the corresponding system of variational inequalities. Our results are of a quasi-explicit nature. From a financial viewpoint, we characterize situations where a firm manager decides optimally to postpone dividend distribution in order to invest in a reversible growth opportunity corresponding to a modern technology. In this paper a reversible opportunity means that the firm may disinvest from the modern technology and return back to its old technology by receiving some gain compensation. The results of our analysis take qualitatively different forms depending on the parameters values.Comment: Published in at http://dx.doi.org/10.1214/07-AAP482 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scalable embedding of multiple perspectives for indefinite life-science data analysis

Life science data analysis frequently encounters particular challenges that cannot be solved with classical techniques from data analytics or machine learning domains. The complex inherent structure of the data and especially the encoding in non-standard ways, e.g., as genome- or protein-sequences, graph structure or histograms, often limit the development of appropriate classification models. To address these limitations, the application of domain-specific expert similarity measures has gained a lot of attention in the past. However, the use of such expert measures suffers from two major drawbacks: (a) there is not one outstanding similarity measure that guarantees success in all application scenarios, and (b) such similarity functions often lead to indefinite data that cannot be processed by classical machine learning methods. In order to tackle both of these limitations, this paper presents a method to embed indefinite life science data with various similarity measures at the same time into a complex-valued vector space. We test our approach on various life science data sets and evaluate the performance against other competitive methods to show its efficiency

Three-Dimensional Radiative Transfer on a Massively Parallel Computer.

We perform three-dimensional radiative transfer calculations on the MasPar MP-1, which contains 8192 processors and is a single instruction multiple data (SIMD) machine, an example of the new generation of massively parallel computers. To make radiative transfer calculations efficient, we must re-consider the numerical methods and methods of storage of data that have been used with serial machines. We developed a numerical code which efficiently calculates images and spectra of astrophysical systems as seen from different viewing directions and at different wavelengths. We use this code to examine a number of different astrophysical systems. First we image the HI distribution of model galaxies. Then we investigate the galaxy NGC 5055, which displays a radial asymmetry in its optical appearance. This can be explained by the presence of dust in the outer HI disk far beyond the optical disk. As the formation of dust is connected to the presence of stars, the existence of dust in outer regions of this galaxy could have consequences for star formation at a time when this galaxy was just forming. Next we use the code for polarized radiative transfer. We first discuss the numerical computation of the required cyclotron opacities and use them to calculate spectra of AM Her systems, binaries containing accreting magnetic white dwarfs. Then we obtain spectra of an extended polar cap. Previous calculations did not consider the three-dimensional extension of the shock. We find that this results in a significant underestimate of the radiation emitted in the shock. Next we calculate the spectrum of the intermediate polar RE 0751+14. For this system we obtain a magnetic field of $\sim$10 MG, which has consequences for the evolution of intermediate polars. Finally we perform 3D radiative transfer in NLTE in the two-level atom approximation. To solve the transfer equation in this case, we adapt the short characteristic method and examine different acceleration methods to obtain the source function. These include the ALI method with local and non-local operators, the Ng and the orthomin methods and multi-grid methods. We apply these numerical methods to two problems with and without periodic boundary conditions

Bid-ask spread modelling, a perturbation approach

Our objective is to study liquidity risk, in particular the so-called ``bid-ask spread'', as a by-product of market uncertainties. ``Bid-ask spread'', and more generally ``limit order books'' describe the existence of different sell and buy prices, which we explain by using different risk aversions of market participants. The risky asset follows a diffusion process governed by a Brownian motion which is uncertain. We use the error theory with Dirichlet forms to formalize the notion of uncertainty on the Brownian motion. This uncertainty generates noises on the trajectories of the underlying asset and we use these noises to expound the presence of bid-ask spreads. In addition, we prove that these noises also have direct impacts on the mid-price of the risky asset. We further enrich our studies with the resolution of an optimal liquidation problem under these liquidity uncertainties and market impacts. To complete our analysis, some numerical results will be provided