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The American early exercise constraint can be viewed as transforming the two dimensional stochastic volatility option pricing PDE into a diierential algebraic equation (DAE). Several methods are described for forcing the algebraic constraint by using a penalty source term in the discrete equations. The resulting nonlinear algebraic equations are solved(More)
The convergence of a penalty method for solving the discrete regularized American option valuation problem is studied. Sufficient conditions are derived which both guarantee convergence of the nonlinear penalty iteration and ensure that the iterates converge monotonically to the solution. These conditions also ensure that the solution of the penalty problem(More)
Many nonlinear option pricing problems can be formulated as optimal control problems, leading to Hamilton-Jacobi-Bellman (HJB) or Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations. We show that such formulations are very convenient for developing monotone discretization methods which ensure convergence to the financially relevant solution, which in this case(More)
Extracellular proteases are crucial regulators of cell function. The family of matrix metalloproteinases (MMPs) has classically been described in the context of extracel-lular matrix (ECM) remodelling, which occurs throughout life in diverse processes that range from tissue mor-phogenesis to wound healing. Recent evidence has implicated MMPs in the(More)
The pricing equations derived from uncertain volatility models in finance are often cast in the form of nonlinear partial differential equations. Implicit timestepping leads to a set of nonlinear algebraic equations which must be solved at each timestep. To solve these equations, an iterative approach is employed. In this paper, we prove the convergence of(More)
A robust numerical method for saturated-unsaturated flow is developed which uses a monotone discretization and variable substitution. This method is compared to a conventional formulation and to a two phase (active air phase) model. On some published test examples of infiltration into dry media, the variable substitution method shows an order of magnitude(More)
Matrix metalloproteinases (MMPs) are increasingly being implicated in the pathogenesis of several CNS diseases. In multiple sclerosis, MMPs could be responsible for the influx of inflammatory mononuclear cells into the CNS, contribute to myelin destruction and disrupt the integrity of the blood-brain barrier; in Alzheimer's disease, MMPs might mediate the(More)
We explore the pricing of Asian options by n umerically solving the the associated partial diierential equations. We demonstrate that numerical PDE techniques commonly used in nance for standard options are inaccurate in the case of Asian options and illustrate mod-iications which alleviate this problem. In particular, the usual methods generally produce(More)
In order to ensure convergence to the viscosity solution, the standard method for discretizing HJB PDEs uses forward/backward differencing for the drift term. In this paper, we devise a monotone method which uses central weighting as much as possible. In order to solve the discretized algebraic equations, we have to maximize a possibly discontinuous(More)
OBJECTIVE This analysis was performed to assess whether antiepileptic drugs (AEDs) modulate the effectiveness of temozolomide radiochemotherapy in patients with newly diagnosed glioblastoma. METHODS The European Organization for Research and Treatment of Cancer (EORTC) 26981-22981/National Cancer Institute of Canada (NCIC) CE.3 clinical trial database of(More)