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

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-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

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

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

Mechanisms of -induced interleukin-8 expression in human lung epithelial cells-4

<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>ations of several known binding sites for transcription factors. (B) infection increases IL-8 promoter activity in a dose-dependent fashion. The -1481-luciferase construct (40 ng) containing IL-8 promoter spanning -1,481 to +44 bp was transfected into A549 cells, and the cells were subsequently infected with varying concentrations of AA100jm for 48 h before luciferase assay. Luciferase activity is presented as a fold induction relative to the basal level measured in uninfected cells. (C) 5' deletion analysis of the IL-8 promoter. The indicated luciferase reporter constructs (40 ng) derived from the IL-8 promoter were transfected into A549 cells, and the cells were subsequently infected with AA100jm strain (MOI of 100) for 48 h. The activities are expressed relative to that of cells transfected with -50-luc without further treatment, which was defined as 1. Data are mean ± SD values of three independent experiments. *, < 0.05; **, < 0.01 (compared to uninfected cells)

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-8

TUNEL method was analyzed by flow cytometry. The nuclear DNA fragmentation of virulent strain AA100jm-infected cells without (A) and with methyl prednisolone (B), is shown with no-pretreatment/no-stimulation cells (control) (C), and 30 μM mitomycin C-exposed cells without (D) and with methyl prednisolone (E). FS indicates the cell sizes. m-P; methyl prednisolone.<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-12

(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

Mechanisms of -induced interleukin-8 expression in human lung epithelial cells-5

<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>F-κB site in the IL-8 promoter (-133 to +44 bp), linked to the luciferase gene, was mutated. (B) Mutational analysis of the -elements required for -induced IL-8 promoter activity. The indicated wild-type and mutated plasmids (40 ng) were transfected into A549 cells, and the cells were subsequently infected with AA100jm strain (MOI of 100) for 48 h. The activities are expressed relative to that of cells transfected with -133-luc without further treatment, which was defined as 1. Data are mean ± SD values of three independent experiments. (C) Diagram of the constructs used in these experiments. (D) -induced IL-8 gene expression is specific for the NF-κB region of the IL-8 gene. The activities are expressed relative to that of cells transfected with -50-luc without further treatment, which was defined as 1. Data are mean ± SD values of three independent experiments. *, < 0.05; **, < 0.005; #, < 0.001; ##, < 0.0005 (compared to uninfected cells)

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-7

Caspase 3) were detected.<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