We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions of lower value function for the associated games (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI) (the analogue of the HamiltonJacobi-Bellman-Isaacs equation for this setting). We show that the stop...

We study the superhedging problem for American options with completely irregular payoffs in a non-linear and incomplete market model default. give dual representation of seller’s (superhedging) price terms value mixed control/stopping problem, involving suitable set equivalent probability measures. characterize process as minimal supersolution two types reflected BSDEs: constrained one an optio...

In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...

The theory of first-order mean field type differential games examines the systems infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study approximations value function game using solutions model finite-dimensional games. appears as a continuous-time Markov game, i.e., theoretical problem with and dynamics deter...

We propose an adaptive reversible data hiding method with superior visual quality and capacity in which an adaptive generalized difference expansion (AGDE) method is applied to an integer-to-integer subband transform (I2I-ST). I2I-ST performs the reversible subband transform and the AGDE method is a state-of-the-art method of reversible data hiding. The results of experiments we performed objec...

We consider a model for the motion of phase interface in an elastic medium, example, twin boundary martensite. The is given by semilinear parabolic equation with fractional Laplacian as regularizing operator, stemming from interaction front its environment. We show that presence randomly distributed, localized obstacles leads to threshold phenomenon, i.e., stationar...