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Showing 1 to 13 of 13 for “"viscosity solution"”.
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On optimal arbitrage under constraints
… further characterize the upper hedging price as viscosity solution to certain variational inequalities. We, then, use this viscosity solution characterization to study how the imposition of stricter constraints on the market affect the upper hedging price. In particular, if relative arbitrage …
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Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients
<p>In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity …
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On some optimal control problems on networks, stratied domains, and controllability of motion in fluids.
… problems we characterize the limit functions as viscosity solution and maximal subsolution of a suitable Hamilton-Jacobi problem. Secondly, we consider a bi-dimensional multi-domain problem and as done for the problems on network we characterize the limit function as viscosity solution of a …
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The Reflected Quasipotential: Characterization and Exploration
The Reflected Quasipotential V(x) is the solution to a variational problem that arises in the study of reflective Brownian motion. Specifically, the stationary distributions of reflected Brownian motion satisfy a large deviation principle (with respect to a spatial scaling parameter) with V(x) as …
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A WENO finite difference scheme for a new class of Hamilton-Jacobi equations in electroelastostatics
… finite difference method converges to the viscosity solution of a special class of Hamilton-Jacobi equations. From then on several successful methods of high-order approximation have been proposed in the literature, including the so-called WENO finite difference schemes. These schemes, …
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Dissipative systems theory : analysis and synthesis
… inequality and looks for an appropriate solution to it. When such a solution exists, one then constructs the desired system by using this solution. The main theme of the thesis is the development of a framework for general dissipative systems analysis and synthesis. We firstly present a …
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Dissipative systems theory : analysis and synthesis
… inequality and looks for an appropriate solution to it. When such a solution exists, one then constructs the desired system by using this solution. The main theme of the thesis is the development of a framework for general dissipative systems analysis and synthesis. We firstly present a …
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Superreplication method for multi-asset barrier options.
… We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving …
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On some Two-Dimensional Singular Stochastic Control Problems and their Free-Boundary Analysis
… optimal dividend strategy can be expressed as a solution to a Skorokhod reflection problem at the free-boundary. In Section 3, an application of the dynamic programming principle is used to derive a system of non-linear equations characterizing the constant free-boundaries. This system is solved …
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Shortest Path Problems: Domain Restriction, Anytime Planning, and Multi-objective Optimization
… practitioners are often only interested in the solution at one specific source point, i.e. the shortest path to the exit-set from a particular starting location. This thesis will focus on three separate, but related, problems of this form. We employ solution methods that discretize the …
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ADVANCES IN STOCHASTIC ANALYSIS ON SPACES OF MEASURES: KOLMOGOROV EQUATIONS RELATED TO STOCHASTIC FILTERING AND MEAN FIELD OPTIMAL STOPPING
Lo scopo di questa Tesi è di studiare alcuni problemi di analisi stocastica e controllo ottimo stocastico, dove alcune variabili prendono valore in spazi di misure positive e di probabilità. La maggior parte del lavoro è dedicata all'introduzione e allo studio di alcune equazioni di Kolmogorov …
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ADVANCES IN MEAN-FIELD OPTIMAL CONTROL VIA DYNAMIC PROGRAMMING EQUATIONS
In questa tesi di dottorato ci proponiamo di analizzare varie classi di problemi di controllo ottimo di tipo McKean-Vlasov con un approccio analitico, che consiste nella caratterizzazione della funzione valore di ciascun problema mediante un'opportuna equazione alle derivate parziali, detta …