Impulse Control in Finance: Numerical Methods and Viscosity Solutions

The goal of this thesis is to provide efficient and provably convergent numerical methods for solving partial differential equations (PDEs) coming from impulse control problems motivated by finance. Impulses, which are controlled jumps in a stochastic process, are used to model realistic features in financial problems which cannot be captured by ordinary stochastic controls. The dynamic programming equations associated with impulse control problems are Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) Other than in certain special cases, the numerical schemes that come from the discretization of HJBQVIs take the form of complicated nonlinear matrix equations also known as Bellman problems. We prove that a policy iteration algorithm can be used to compute their solutions. In order to do so, we employ the theory of weakly chained diagonally dominant (w.c.d.d.) matrices. As a byproduct of our analysis, we obtain some new results regarding a particular family of Markov decision processes which can be thought of as impulse control problems on a discrete state space and the relationship between w.c.d.d. matrices and M-matrices. Since HJBQVIs are nonlocal PDEs, we are unable to directly use the seminal result of Barles and Souganidis (concerning the convergence of monotone, stable, and consistent numerical schemes to the viscosity solution) to prove the convergence of our schemes. We address this issue by extending the work of Barles and Souganidis to nonlocal PDEs in a manner general enough to apply to HJBQVIs. We apply our schemes to compute the solutions of various classical problems from finance concerning optimal control of the exchange rate, optimal consumption with fixed and proportional transaction costs, and guaranteed minimum withdrawal benefits in variable annuities

Patient background.

<p>Patient background.</p

Causative species of nontuberculous mycobacterial lung disease and comparative investigation on clinical features of <i>Mycobacterium abscessus</i> complex disease: A retrospective analysis for two major hospitals in a subtropical region of Japan

<div><p>Nontuberculous mycobacteria (NTM) lung disease is increasing globally. Although the etiological epidemiology of NTM is different across regions, <i>Mycobacterium avium</i> complex (MAC) is the leading cause of NTM lung disease in most countries, including mainland Japan. Okinawa is located in the southernmost region of Japan and is the only prefecture categorized as a subtropical region in Japan, it is therefore likely the etiological epidemiology of NTM lung disease is different from mainland Japan. From 2009 to 2015, the medical records of patients, with respiratory specimens positive for NTMs, visiting or admitted to two Okinawan hospitals, were retrospectively analyzed. NTM lung disease cases were defined according to the American Thoracic Society criteria and patient epidemiology and clinical information were evaluated. Results indicate four hundred sixteen patients had bacterial cultures positive for NTM. The most common NTM was <i>M</i>. <i>abscessus</i> complex (MABC) (n = 127; 30.5%), followed by <i>M</i>. <i>intracellulare</i> (n = 85; 20.4%). NTM lung disease was diagnosed in 114 patients. Of these cases, MABC was most common (n = 41; 36.0%), followed by <i>M</i>. <i>intracellulare</i> (n = 31; 27.2%). Chronic obstructive pulmonary disease (COPD) and tracheostomy patients were more likely to develop MABC than MAC lung disease. Multivariate analysis showed a probable association between COPD and MABC lung disease. Chest computed tomography (CT) evaluation revealed bronchiectasis, nodules, and consolidation were less frequently observed in MABC patients compared with MAC patients. Our data suggests Okinawa may be one of the few places where MABC is the predominant pathogen causing NTM lung disease and our results add new insight to MABC lung disease, which is not yet well understood.</p></div

NTMs cultured from respiratory samples (N = 416).

<p>NTMs isolated from respiratory specimens were retrospectively analyzed. Others category includes: <i>Mycobacterium kansasii</i> (1.0%), <i>M</i>. <i>szulgai</i> (0.7%), <i>M</i>. <i>xenopi</i> (0.7%), <i>M</i>. <i>peregrium</i> (0.5%), <i>M</i>. <i>scrofulaceum</i> (0.5%), <i>M</i>. <i>simiae</i> (0.2%), and <i>M</i>. <i>terrae</i> (0.2%).</p

Additional file 2: Table 1. of Comparative epidemiology of influenza A and B viral infection in a subtropical region: a 7-year surveillance in Okinawa, Japan

Example weeks from dataset 1 and dataset 2 post-alignment. Sample weeks shown here are to serve as a visual representation of the method outlined to evaluate age distribution. Dataset 1 (left) and dataset 2 (right) were combined and aligned following the selection of “epidemic weeks”. A week in which influenza A or B cases accounted for more than 90 % of all positive influenza cases was defined as an epidemic week. In the year 2007, you see an example of a defined influenza A epidemic week, whereas the year 2011 is a representative influenza B epidemic week. The week from 2013 displays a typical week which was removed from our age distribution analysis because neither influenza A nor B was dominant (>90 %). (PPTX 66 kb

Multivariate analysis to determine clinical charecteristics for MABC.

<p>Multivariate analysis to determine clinical charecteristics for MABC.</p

Infection induces programmed cell death, caspase activation, and release of high-mobility group box 1 protein in A549 alveolar epithelial cells: inhibition by methyl prednisolone-4

Ed high-power fields, and TUNEL-positive cells were expressed as a ratio per total number of cells. Symbols: ▫, virulent strain AA100jm; ▪, avirulent strain mutant. Data are mean ± SD of three different experiments. * < 0.05.<p><b>Copyright information:</b></p><p>Taken from "infection induces programmed cell death, caspase activation, and release of high-mobility group box 1 protein in A549 alveolar epithelial cells: inhibition by methyl prednisolone"</p><p>Respiratory Research 2008;9(1):39-39.</p><p>Published online 1 May 2008</p><p>PMCID:PMC2390540.</p><p></p

Mechanisms of -induced interleukin-8 expression in human lung epithelial cells-8

<p><b>Copyright information:</b></p><p>Taken from "Mechanisms of -induced interleukin-8 expression in human lung epithelial cells"</p><p>http://www.biomedcentral.com/1471-2180/7/102</p><p>BMC Microbiology 2007;7():102-102.</p><p>Published online 22 Nov 2007</p><p>PMCID:PMC2213657.</p><p></p> varying concentrations of AA100jm strain for 6 h. RT-PCR was performed to check the changes of IL-8 mRNA expression after 17-AAG treatment in -infected A549 cells. (B) Attenuation of -induced NF-κB DNA binding by 17-AAG treatment. A549 cells were treated with (+) or without (-) 17-AAG for 16 h prior to infection with varying concentrations of for 3 h. The nuclear extracts were isolated from A549 cells infected with and incubated with P-labeled oligonucleotides corresponding to NF-κB. (C) hsp90 protects IKKα and IKKβ from proteasomal degradation. A549 cells either were pretreated with LLnL (20 μM) for 1 h, followed or not followed by addition of 17-AAG (1 μM) and incubation for 16 h, or were treated with 17-AAG for 16 h or left untreated as indicated. Whole cell extracts were immunoblotted with specific antibodies against each protein. Representative results of three similar experiments in each panel are shown

Infection induces programmed cell death, caspase activation, and release of high-mobility group box 1 protein in A549 alveolar epithelial cells: inhibition by methyl prednisolone-1

0 (A), and an MOI dose-response relationship 2 days after infection (B). Symbols : ▫, virulent strain AA100jm; ▪, avirulent strain mutant. Data are mean ± SD of three wells. * < 0.05.<p><b>Copyright information:</b></p><p>Taken from "infection induces programmed cell death, caspase activation, and release of high-mobility group box 1 protein in A549 alveolar epithelial cells: inhibition by methyl prednisolone"</p><p>Respiratory Research 2008;9(1):39-39.</p><p>Published online 1 May 2008</p><p>PMCID:PMC2390540.</p><p></p

Infection induces programmed cell death, caspase activation, and release of high-mobility group box 1 protein in A549 alveolar epithelial cells: inhibition by methyl prednisolone-13

infection. Symbols : ▫, virulent strain AA100jm; ▪, avirulent strain mutant. Data are mean ± SD of three wells. * < 0.05.<p><b>Copyright information:</b></p><p>Taken from "infection induces programmed cell death, caspase activation, and release of high-mobility group box 1 protein in A549 alveolar epithelial cells: inhibition by methyl prednisolone"</p><p>Respiratory Research 2008;9(1):39-39.</p><p>Published online 1 May 2008</p><p>PMCID:PMC2390540.</p><p></p