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

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

Viscosity Solutions for a System of PDEs and Optimal Switching

In this paper, we study the $m$-states optimal switching problem in finite horizon, when the switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central evaluation in cases where such organizations or state grants or financial assistance to power plants that promotes green energy in their production activity or what uses less polluting modes in their production. We show existence for optimal strategy via a verification theorem then we show existence and uniqueness of the value processes by using an approximation scheme. In the markovian framework we show that the value processes can be characterized in terms of deterministic continuous functions of the state of the process. Those latter functions are the unique viscosity solutions for a system of $m$ variational partial differential inequalities with inter-connected obstacles.Comment: 26 pages. arXiv admin note: substantial text overlap with arXiv:1102.1256, arXiv:0805.1306, arXiv:0904.0707, arXiv:1202.1108, and arXiv:0707.2663 and arXiv:1104.2689 by other authors. IMA Journal of Mathematical Control and Information (2016

A 3D radiative transfer framework: I. non-local operator splitting and continuum scattering problems

We describe a highly flexible framework to solve 3D radiation transfer problems in scattering dominated environments based on a long characteristics piece-wise parabolic formal solution and an operator splitting method. We find that the linear systems are efficiently solved with iterative solvers such as Gauss-Seidel and Jordan techniques. We use a sphere-in-a-box test model to compare the 3D results to 1D solutions in order to assess the accuracy of the method. We have implemented the method for static media, however, it can be used to solve problems in the Eulerian-frame for media with low velocity fields.Comment: A&A, in press. 14 pages, 19 figures. Full resolution figures available at ftp://phoenix.hs.uni-hamburg.de/preprints/3DRT_paper1.pdf HTML version (low res figures) at http://hobbes.hs.uni-hamburg.de/~yeti/PAPERS/3drt_paper1/index.htm

The accretion flow in the discless intermediate polar V2400 Ophiuchi

RXTE observations confirm that the X-ray lightcurve of V2400 Oph is pulsed at the beat cycle, as expected in a discless intermediate polar. There are no X-ray modulations at the orbital or spin cycles, but optical line profiles vary with all three cycles. We construct a model for line-profile variations in a discless accretor, based on the idea that the accretion stream flips from one magnetic pole to the other, and show that this accounts for the observed behaviour over the spin and beat cycles. The minimal variability over the orbital cycle implies that 1) V2400 Oph is at an inclination of only ~10 deg, and 2) much of the accretion flow is not in a coherent stream, but is circling the white dwarf, possibly as a ring of denser, diamagnetic blobs. We discuss the light this sheds on disc formation in intermediate polars.Comment: 10 pages, 12 figures, To appear in MNRAS, includes low-res figures to reduce siz

High-Conflict Divorce: An Evaluation of New Ways for Families

High-conflict divorces have increased in the past two decades. They can include poor communication, low problem solving skills, aggressive, and violent behaviours. When they involve minor children there is an increased social concern. Children exposed to high-conflict can experience short and long-term negative biopsychosocial outcomes. Professionals (i.e., the courts and social agencies) involved in high-conflict families struggle to provide effective supports. The current thesis aims to evaluate the counselling intervention: New Ways for Families for divorcing co-parents going through a high-conflict divorce. The Ribner Scale, developed by Neil Ribner, was used to measure pre- and post- intervention levels on the factors associated with high-conflict divorce: (a) perceived inter-parental conflict; (b) communication; (c) co-operation and (c) continuous litigation; With an inclusion of violence to explore its overlapping role with high-conflict. In addition, this thesis will add to the knowledge base around the demographics of former couples involved in a high-conflict divorce.2022-0

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

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