We study invariance and viability properties of a closed set for the trajectories of either a controlled diiusion process or a controlled deterministic system with disturbances. We use the value functions associated to suitable optimal control problems or diierential games and analyze the related Dynamic Programming equation within the theory of viscosity solutions.

In this paper we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a “renewal” process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the b...

2 Deterministic Dynamic Programming and Viscosity Solutions 5 2.

Following the framework of Çetin, Jarrow and Protter [4] we study the problem of super-replication in presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized Black-Scholes economy. We find that the minimal super-replication price is different from the one suggested by the Black-Scholes formula and is the unique viscosity solution of the ...

We consider a class of singularly perturbed zero-sum diier-ential games with piecewise deterministic dynamics, where the changes from one structure (for the dynamics) to another are governed by a nite-state Markov process. Player 1 controls the continuous dynamics, whereas Player 2 controls the rate of transition for the nite-state Markov process; both have access to the states of both processe...

Objective (s): Artificial Neural Networks (ANN) are widely used for predicting systems’ behavior. GMDH is a type of ANNs which has remarkable ability in pattern recognition. The aim the current study is proposing a model to predict dynamic viscosity of silver/water nanofluid which can be used as antimicrobial fluid in several medical purposes.Materials and Methods: In order to have precise mode...

In this work, a simultaneous modeling of the self-diffusion coefficient and the dynamic viscosity is presented. In the microstructural theory these two quantities are governed by the same friction coefficient related to the mobility of the molecule. A recent free-volume model, already successfully applied to dynamic viscosity, has been considered and generalized. In this generalized model the c...

S U M M A R Y Our understanding of mantle convection and the motion of plates depends intimately on our understanding of the viscosity structure of the mantle. While geoid and gravity observations have provided fundamental constraints on the radial viscosity structure of the mantle, the influence of short-wavelength variations in viscosity is still poorly understood. We present 2-D and 3-D fini...