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

Electronic supplemental information from Multi-functional roles of a soldier-specific volatile as a worker arrestant, primer pheromone and an antimicrobial agent in a termite

Supplementary figure

Electronic supplemental information from Multi-functional roles of a soldier-specific volatile as a worker arrestant, primer pheromone and an antimicrobial agent in a termite

Supplementary figure

Synthesis of (−)-Chamobtusin A from (+)-Dehydroabietylamine

Chamobtusin A, a unique diterpene alkaloid isolated from Chamaecyparis obtusa cv. tetragon, is considered to be biosynthesized from an abietane diterpenoid. On the basis of this biosynthetic hypothesis, ferruginol (<b>15</b>) was synthesized from (+)-dehydroabietylamine and then biomimetically transformed into (−)-chamobtusin A in 6 steps (12 steps from (+)-dehydroabietylamine)

Enantioselective Total Synthesis of (+)-Anthecularin

An enantioselective total synthesis of (+)-anthecularin, an antiplasmodial and antitrypanosomal sesquiterpene lactone, has been achieved in 3.9% overall yield through 18 steps from a known dibromo alcohol. The key features of the synthesis include an intramolecular Claisen-type cyclization of a formyl-protected hydroxyl lactone to construct a bicyclic intermediate with a quaternary stereogenic center and a stereocontrolled 1,2-addition of vinyllithium to a methoxyethyl-protected spirocyclic hydroxyl enone to install a tetrasubstituted asymmetric center with excellent diastereoselection. This first enantioselective synthesis of anthecularin enabled the determination of its absolute configuration as 2<i>R</i>, 3<i>R</i>, 4<i>S</i>, 8<i>R</i>

Induced phenylamide accumulation in response to pathogen infection and hormone treatment in rice (<i>Oryza sativa</i>)

<p>Rice plants accumulate various specialized metabolites, including phenylamides, in response to pathogen attack. We prepared 25 phenylamides, and developed a method of analyzing them by multiple reaction monitoring with liquid chromatography coupled with tandem mass spectrometry. We analyzed phenylamides in rice leaves infected with <i>Cochliobolus miyabeanus</i> and <i>Xanthomonas oryzae</i>. The phenylamides induced included benzoyltryptamine, cinnamoyl-, <i>p</i>-coumaroyl-, feruloyl-, and benzoylserotonins, cinnamoyl and benzoyltyramines, feruloylagmatine, and feruloylputrescine. Some of the phenylamides exhibited antimicrobial activity against <i>C. miyabeanus</i> and <i>X. oryzae</i>, indicating that they are phytoalexins. Treatment with jasmonic acid, salicylic acid, 6-benzylaminopurine, and ethephone also induced phenylamide accumulation. The compositions of the induced amides varied depending on the plant hormone used, and cinnamoyltryptamine, cinnamoylserotonin, and cinnamoyltyramine were not induced by the plant hormones. These findings suggest that several plant hormones and additional factors are involved in phenylamide accumulation in response to pathogen infection in rice.</p> <p>Rice plant accumulates phenylamides in response to infection, wounding and treatments with jasmonic acid, salycilic acid, cytokinin, and ethylene.</p

A fragmentation study of isoflavones by IT-TOF-MS using biosynthesized isotopes

<p>To aid in the identification and quantification of biologically and agriculturally significant natural products, tandem mass spectrometry can provide accurate structural information with high selectivity and sensitivity. In this study, diagnostic fragmentation patterns of isoflavonoids were examined by liquid chromatography-ion trap-time of flight-mass spectrometry (LC-IT-TOF-MS). The fragmentation scheme for [M+H−2CO]⁺ ions derived from isoflavones and [M+H−B-ring−CO]⁺ ions derived from 5-hydroxyisoflavones, were investigated using different isotopically labeled isoflavones, specifically [1′,2′,3′,4′,5′,6′,2,3,4-¹³C₉] and [2′,3′,5′,6′,2-D₅] isoflavones. Specific isotopically labeled isoflavones were prepared through the biosynthetic incorporation of pharmacologically applied ¹³C- and D-labelled L-phenylalanine precursors in soybean plants following the application of insect elicitors. Using this approach, we empirically demonstrate that the [M+H−2CO]⁺ ion is generated by an intramolecular proton rearrangement during fragmentation. Furthermore, [M+H−B-ring−CO]⁺ ion is demonstrated to contain a C₂H moiety derived from C-ring of 5-hydroxyisoflavones. A mechanistic understanding of characteristic isoflavone fragmentation patterns contributes to the efficacy and confidence in identifying related isoflavones by LC-MSⁿ.</p> <p>The fragmentation pattern of isotopically labeled isoflavones, which were prepared by the treatment with the combination of isotopically labeled phenylalanine and insect-derived elicitors, was investigated by LC-IT-TOF-MS.</p

Allele-specific polymerase chain reaction (AS-PCR) of the <i>MYD88</i> gene in Waldenström’s macroglobulinemia and lymphoma.

<div><p>Ten μl of PCR products was separated by electrophoresis through a 2% agarose gel, stained with ethidium bromide, and visualized by ultraviolet illumination. The size of the products is indicated on the left.</p> <p>(A) Sensitivity of AS-PCR. L265P-positive DNA (WM5) was diluted into wild-type DNA (WM2) before amplification. Mutations were detected in samples containing 0.1% or more of the L265P mutation. Lane 1, 100 bp ladder; lane 2, 0%; lane 3, 0.1%; lane 4, 0.5%; lane 5, 1%; lane 6, 0%; lane 7, 0.1%; lane 8, 0.5%; lane 9, 1%.</p> <p>(B) Aberrant bands were detected in 12 of 16 samples from WM patients (lanes 2, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, and 17). Lane 1, 100 bp ladder; lane 2, WM1; lane 3, WM2; lane 4, WM3; lane 5, WM4; lane 6, WM5; lane 7, WM6; lane 8, WM7; lane 9, WM8; lane 10, WM9; lane 11, WM10; lane 12, WM11; lane 13, WM12, lane 14, WM13; lane 15, WM14; lane 16, WM15; lane 17, WM16.</p> <p>(C) Aberrant bands were detected in 6 of 10 samples from WM patients (lanes 2, 3, 6, 7, 8, and 10) and 2 of 3 non-Hodgkin’s lymphoma patients (lanes 12 and 13). Lane 1, 100 bp ladder; lane 2, WM17; lane 3, WM18; lane 4, WM19; lane 5, WM20; lane 6, WM21; lane 7, WM22; lane 8, WM23; lane 9, WM24; lane 10, WM25; lane 11, NHL1; lane 12, NHL2; lane 13, NHL3; lane 14, normal lymphocyte; lane 15, water.</p></div

Location of the analyzed mutation and a schema of the involved pathway.

<p>TIRAP, TIR domain containing adaptor protein; IRAK, IL-1 receptor-associated kinase; BTK, Bruton’s tyrosine kinase; TRAF, tumor necrosis factor receptor-associated factor; TAK, TGF-β-activated kinase; TAB, TAK binding protein; IκB, inhibitor κB; IKK, IκB kinase; NF-κB, nuclear factor-κB.</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