Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

Dynamic programming for stochastic target problems, Viscosity solutions and hedging in markets with Portfolio constraints and large investors

The purpose of this expository arti le is to present a self- ontained overview of some results on the hara terization of the optimal value fun tion of a sto hasti target problem as (dis ontinuous) vis osity solution of a ertain dynami programming PDE and its appli ation to the problem of hedging ontingent laims in the presen e of portfolio onstraints and large investors

Les processus additifs markoviens et leurs applications en finance mathématique

Cette thèse porte sur les questions d'évaluation et de couverture des options dans un modèle exponentiel-Lévy avec changements de régime. Un tel modèle est construit sur un processus additif markovien un peu comme le modèle de Black- Scholes est basé sur un mouvement Brownien. Du fait de l'existence de plusieurs sources d'aléa, nous sommes en présence d'un marché incomplet et ce fait rend inopérant les développements théoriques initiés par Black et Scholes et Merton dans le cadre d'un marché complet. Nous montrons dans cette thèse que l'utilisation de certains résultats de la théorie des processus additifs markoviens permet d'apporter des solutions aux problèmes d'évaluation et de couverture des options. Notamment, nous arrivons à caracté- riser la mesure martingale qui minimise l'entropie relative à la mesure de probabilit é historique ; aussi nous dérivons explicitement sous certaines conditions, le portefeuille optimal qui permet à un agent de minimiser localement le risque quadratique associé. Par ailleurs, dans une perspective plus pratique nous caract érisons le prix d'une option Européenne comme l'unique solution de viscosité d'un système d'équations intégro-di érentielles non-linéaires. Il s'agit là d'un premier pas pour la construction des schémas numériques pour approcher ledit prix.

Ecuaciones diferenciales estocásticas con condición final y soluciones de viscosidad de EDPS semilineales de segundo orden

El objetivo de este documento es recopilar algunos resultados clasicos sobre existencia y unicidad ´ de soluciones de ecuaciones diferenciales estocasticas (EDEs) con condici ´ on final (en ingl ´ es´ Backward stochastic differential equations) con particular enfasis en el caso de coeficientes mon ´ otonos, y su cone- ´ xion con soluciones de viscosidad de sistemas de ecuaciones diferenciales parciales (EDPs) parab ´ olicas ´ y el´ıpticas semilineales de segundo orden.

Portifolio selection with random transaction costs

Transaction costs have a random component in the bid-ask spread. Facing a high bid-ask spread, the consumer has the option to wait for better terms oI' trade, but only by carrying an undesirable portfolio balance. We present the best policy in this case. We pose the control problem and show that the value function is the uni que viscosity solution of the relevant variational inequality. Next, a numerical procedure for the problem is presented.

Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

The Effects of Credit Risk on Dynamic Portfolio Management: A New Computational Approach

The study investigates the role of credit risk in a continuous time stochastic asset allocation model, since the traditional dynamic framework does not provide credit risk flexibility. The general model of the study extends the traditional dynamic efficiency framework by explicitly deriving the optimal value function for the infinite horizon stochastic control problem via a weighted volatility measure of market and credit risk. The model's optimal strategy was then compared to that obtained from a benchmark Markowitz-type dynamic optimization framework to determine which specification adequately reflects the optimal terminal investment returns and strategy under credit and market risks. The paper shows that an investor's optimal terminal return is lower than typically indicated under the traditional mean-variance framework during periods of elevated credit risk. Hence I conclude that, while the traditional dynamic mean-variance approach may indicate the ideal, in the presence of credit-risk it does not accurately reflect the observed optimal returns, terminal wealth and portfolio selection strategies.

Influence of the concentration of Sb2O3 and the viscosity of the precursor solution on the electrical and optical properties of SnO2 thin films produced by the Pechini method

SnO2:Sb multi-layer coatings were prepared by the Pechini method. An investigation was made of the influence of the concentration of Sb2O3 and the viscosity of the precursor solution on the electrical and optical properties of SnO2 thin films. The use of a multi-layer system as an alternative form of increasing the packing and. thus. decreasing porosity proved to be efficient, decreasing the system's resistivity without altering its optical properties. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Whole body postmortem angiography with a high viscosity contrast agent solution using poly ethylene glycol as contrast agent dissolver

Postmortem minimal invasive angiography has already been implemented to support virtual autopsy examinations. An experimental approach in a porcine model to overcome an initially described artificial tissue edema artifact by using a poly ethylene glycol (PEG) containing contrast agent solution showed promising results. The present publication describes the first application of PEG in a whole corpse angiographic CT examination. A minimal invasive postmortem CT angiography was performed in a human corpse utilizing the high viscosity contrast agent solution containing 65% of PEG. Injection was carried out via the femoral artery into the aortic root in simulated cardiac output conditions. Subsequent CT scanning delivered the 3D volume data of the whole corpse. Visualization of the human arterial anatomy was excellent and the contrast agent distribution was generally limited to the arterial system as intended. As exceptions an enhancement of the brain, the left ventricular myocardium and the renal cortex became obvious. This most likely represented the stage of centralization of the blood circulation at the time of death with dilatation of the precapillary arterioles within these tissues. Especially for the brain this resulted in a distinctively improved visualization of the intracerebral structures by CT. However, the general tissue edema artifact of postmortem minimal invasive angiography examinations could be distinctively reduced.

Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Determination of viscosity of some Australian honeys based on composition

Rheological properties of four unprocessed unifloral Australian honeys (heath, tea tree, yapunya, and yellow box) and an artificial honey were analysed at 20degreesC. A model previously used to describe viscosity data of various sugar and sugar mixtures was used to describe the concentration dependence of the viscosity of honey samples with varying moisture contents. The model successfully described the sugar concentration dependence of the unadulterated and medium moisture (70-85% solids) range honey samples.

Reaction Kinetics and Viscosity Modelling in the Fusion Syntheses of Ca- and Ca/Mg-resinates

Rosin is a natural product from pine forests and it is used as a raw material in resinate syntheses. Resinates are polyvalent metal salts of rosin acids and especially Ca- and Ca/Mg- resinates find wide application in the printing ink industry. In this thesis, analytical methods were applied to increase general knowledge of resinate chemistry and the reaction kinetics was studied in order to model the non linear solution viscosity increase during resinate syntheses by the fusion method. Solution viscosity in toluene is an important quality factor for resinates to be used in printing inks. The concept of critical resinate concentration, c crit, was introduced to define an abrupt change in viscosity dependence on resinate concentration in the solution. The concept was then used to explain the non-inear solution viscosity increase during resinate syntheses. A semi empirical model with two estimated parameters was derived for the viscosity increase on the basis of apparent reaction kinetics. The model was used to control the viscosity and to predict the total reaction time of the resinate process. The kinetic data from the complex reaction media was obtained by acid value titration and by FTIR spectroscopic analyses using a conventional calibration method to measure the resinate concentration and the concentration of free rosin acids. A multivariate calibration method was successfully applied to make partial least square (PLS) models for monitoring acid value and solution viscosity in both mid-infrared (MIR) and near infrared (NIR) regions during the syntheses. The calibration models can be used for on line resinate process monitoring. In kinetic studies, two main reaction steps were observed during the syntheses. First a fast irreversible resination reaction occurs at 235 °C and then a slow thermal decarboxylation of rosin acids starts to take place at 265 °C. Rosin oil is formed during the decarboxylation reaction step causing significant mass loss as the rosin oil evaporates from the system while the viscosity increases to the target level. The mass balance of the syntheses was determined based on the resinate concentration increase during the decarboxylation reaction step. A mechanistic study of the decarboxylation reaction was based on the observation that resinate molecules are partly solvated by rosin acids during the syntheses. Different decarboxylation mechanisms were proposed for the free and solvating rosin acids. The deduced kinetic model supported the analytical data of the syntheses in a wide resinate concentration region, over a wide range of viscosity values and at different reaction temperatures. In addition, the application of the kinetic model to the modified resinate syntheses gave a good fit. A novel synthesis method with the addition of decarboxylated rosin (i.e. rosin oil) to the reaction mixture was introduced. The conversion of rosin acid to resinate was increased to the level necessary to obtain the target viscosity for the product at 235 °C. Due to a lower reaction temperature than in traditional fusion synthesis at 265 °C, thermal decarboxylation is avoided. As a consequence, the mass yield of the resinate syntheses can be increased from ca. 70% to almost 100% by recycling the added rosin oil.

Solution behavior and surface properties of carboxymethylcellulose acetate butyrate

Solution behavior of carboxymethylcellulose acetate butyrate (CMCAB) in acetone and ethyl acetate has been investigated by small-angle X-ray scattering (SAXS) and capillary viscometry and correlated with the characteristics of CMCAB films. Viscosity and SAXS measurements showed that ethyl acetate is a better solvent than acetone for CMCAB. Thin films of CMCAB were deposited onto silicon wafers (Si/SiO(2)) by spin coating. AFM images revealed that CMCAB spin coated films from solutions prepared in ethyl acetate were homogeneous and flat. However, films obtained from solutions in acetone were very rough. Contact angle measurements with polar and apolar test liquids characterized CMCAB surfaces as hydrophobic and allowed estimating the surface energy of CMCAB. Sum frequency generation vibrational spectroscopy was used to understand the role played by solvents and to gain insight about molecular orientation at Si/SiO(2)/CMCAB interface.