A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

Some Results on the Boundary Control of Systems of Conservation Laws

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions. We first consider the problem of controllability at a fixed time for genuinely nonlinear Temple class systems, and present a description of the set of attainable configurations of the corresponding solutions in terms of suitable Oleinik-type estimates. We next present a result concerning the asymptotic stabilization near a constant state for general $n\times n$ systems. Finally we show with an example that in general one cannot achieve exact controllability to a constant state in finite time.Comment: 10 pages, 4 figures, conferenc

Enhancing the effectiveness of nucleoside analogs with mTORC1 blockers to treat acute myeloid leukemia patients

Powerpoint and speaker's note

Biology matters: the clinical impact of single-receptor discordance on breast cancer

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Estabilidade de agregados de um Latossolo Vermelho sob diferentes plantas de coberturas de inverno e sistemas de preparo do solo.

Os sistemas de manejo agrícolas interferem nas características físicas do solo, principalmente na agregação. O objetivo deste estudo foi avaliar a estabilidade de agregados do solo de um experimento de longa duração com plantas de cobertura de inverno e sistemas de preparo do solo. O experimento teve início no ano de 1986, no Instituto Agronômico do Paraná, em Pato Branco sob um Latossolo Vermelho aluminoférrico. Os tratamentos são uma combinação entre coberturas de solo: aveia preta, centeio, ervilhaca comum, ervilhaca peluda, nabo forrageiro, tremoço azul, trigo e pousio, e sistemas de preparo: plantio direto (PD) e plantio convencional (PC), dispostos em parcelas subdivididas com três repetições. As amostras de solo foram coletadas em 2012, nas profundidades de 0 a 5, 5 a 10 e 10 a 20 cm. A estabilidade de agregados foi determinada através de tamisamento a úmido, e posteriormente calculado o índice de diâmetro médio ponderado (DMP) dos agregados. O PD apresentou maior DMP na profundidade de 0 a 5 cm, enquanto que para o PC, o maior DMP ocorreu de 10 a 20 cm de profundidade. O pousio obteve o menor DMP diferindo das espécies de cobertura de inverno, para o PD de 0 a 5 e 5 a 10 cm de profundidade. A utilização de espécies de cobertura de inverno associada a sistemas conservacionistas de preparo do solo, com mínimo revolvimento, promove maior estabilidade da agregação do solo

Adolescents and primary herpetic gingivostomatitis: an Italian overview

Aim The aim of this study was to investigate the therapies administered to Italian adolescents with primary herpetic gingivostomatitis (PHGS) Methods The medical records of 74 adolescents with PHSG were reviewed. The following data were recorded: age, gender, day of onset, type of treatment, lesions' severity, pain scoring, eating, and drinking ability. The oral examination was performed at the first evaluation (T0) and after one week (T1). Results All patients showed up at the first visit at least 48 h after the onset of symptoms. No patient was prescribed an antiviral therapy. An antibiotic therapy was prescribed in order to prevent secondary bacterial infections. Fifteen patients had been treated with non alcoholic chlorhexidine rinses (group A), 29 patients with non alcoholic chlorhexidine rinses plus hyaluronic acid gel (group B); 30 patients with non alcoholic chlorhexidine rinses plus Mucosyte (R) (group C). A significant improvement of the pain scoring and lesions' severity was noted in group C. Conclusion In Italian adolescents, PHGS is diagnosed at least 48 h after onset and the antibiotic therapy is widely prescribed in order to prevent overinfections. Among topical therapies, an association of verbascoside and sodium hyaluronhate seems to favour a faster healing