Second Order BSDEs with Jumps: Existence and probabilistic representation for fully-nonlinear PIDEs

In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [15]. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of some fully non-linear partial integro-differential equations, which is the point of the second part of this work. We prove a non-linear Feynman-Kac formula and show that solutions to 2BSDEJs provide viscosity solutions of the associated PIDEs.Comment: 39 page

Quadratic BSDEs with jumps: a fixed-point approach

In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z,u). From a technical point of view, we use a direct fixed point approach as in Tevzadze [38], which allows us to obtain existence and uniqueness of a solution when the terminal condition is small enough. Then, thanks to a well-chosen splitting, we recover an existence result for general bounded solution. Under additional assumptions, we can obtain stability results and a comparison theorem, which as usual implies uniqueness.Comment: 29 page

On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples

We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function can be non convex and needs not to satisfy global Lipschitz conditions in the jump integrand. We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a-priori $L^{\infty}$-bounds. Several examples and counter examples are discussed to shed light on the scope and applicability of different assumptions, and we provide an overview of major applications in finance and optimal control.Comment: 28 pages. Added DOI https://link.springer.com/chapter/10.1007%2F978-3-030-22285-7_1 for final publication, corrected typo (missing gamma) in example 4.1

Prediction models of mechanical properties for pet-mortar composite in sodium sulphateaggressive mediums

In this research, an investigation was carried out on the effect of sodium sulphate attack on the durability of composites produced with waste polyethylene terephthalate (PET). Experiments were accomplished on limestone sand and cement mortars where the blended Portland cement was partially replaced by various volume fractions of waste PET particles (6%, 12% and 17%). The test solutions used to supply the sulphate ions and cations were 5%sodium sulphate solution. Compressive strengths measured on specimens were used to assess the changes in the mechanical properties of PET-mortars exposed to sulphate attack at different ages, mainly the Young modulus of elasticity. Based on experimental compressive tests on PETMortar composite specimens and there densities, the evolution of Young modulus of elasticity has been analyzed in accordance with normative models given by (ACI-318) and (BS-8110) codes of practice. In addition, a comparative study has been carried out for corrosion resistance coefficients K of unmodified mortar to those modified with waste PET particles. It can be noticed that, for the composite immersed in a corrosive Na2SO4 solution, the corrosion resistance coefficients decrease with the increase of the immersion period. The corrosion sulphate resistance K based on Young modulus before and after immersion of PET-mortar composites is better than that of the control mortar. Therefore, for safety considerations of PET-mortar composites use, ACI 318 is recommended code for design and investigation works. Also, it can be concluded that adding waste PET by volume fractions (6%, 12% and 17%) to blend Portland cement renders this cement more resistant to the sodium sulphate aggressive medium. Therefore, composites materials based waste PET aare often presented as the materials of the future because of their potential for innovation and the advantages they offer. In fact, using waste PET as cement substitutes reduces the energy consumption. These modified mortars address problems related to environmental pollution by CO2 emissions, and are used to repair various reinforced concrete structures in sodium sulphate aggressive mediums

Prediction models of mechanical properties for pet-mortar composite in sodium sulphateaggressive mediums

In this research, an investigation was carried out on the effect of sodium sulphate attack on the durability of composites produced with waste polyethylene terephthalate (PET). Experiments were accomplished on limestone sand and cement mortars where the blended Portland cement was partially replaced by various volume fractions of waste PET particles (6%, 12% and 17%). The test solutions used to supply the sulphate ions and cations were 5%sodium sulphate solution. Compressive strengths measured on specimens were used to assess the changes in the mechanical properties of PET-mortars exposed to sulphate attack at different ages, mainly the Young modulus of elasticity. Based on experimental compressive tests on PETMortar composite specimens and there densities, the evolution of Young modulus of elasticity has been analyzed in accordance with normative models given by (ACI-318) and (BS-8110) codes of practice. In addition, a comparative study has been carried out for corrosion resistance coefficients K of unmodified mortar to those modified with waste PET particles. It can be noticed that, for the composite immersed in a corrosive Na2SO4 solution, the corrosion resistance coefficients decrease with the increase of the immersion period. The corrosion sulphate resistance K based on Young modulus before and after immersion of PET-mortar composites is better than that of the control mortar. Therefore, for safety considerations of PET-mortar composites use, ACI 318 is recommended code for design and investigation works. Also, it can be concluded that adding waste PET by volume fractions (6%, 12% and 17%) to blend Portland cement renders this cement more resistant to the sodium sulphate aggressive medium. Therefore, composites materials based waste PET aare often presented as the materials of the future because of their potential for innovation and the advantages they offer. In fact, using waste PET as cement substitutes reduces the energy consumption. These modified mortars address problems related to environmental pollution by CO2 emissions, and are used to repair various reinforced concrete structures in sodium sulphate aggressive mediums

Prediction models of mechanical properties for pet-mortar composite in sodium sulphateaggressive mediums

In this research, an investigation was carried out on the effect of sodium sulphate attack on the durability of composites produced with waste polyethylene terephthalate (PET). Experiments were accomplished on limestone sand and cement mortars where the blended Portland cement was partially replaced by various volume fractions of waste PET particles (6%, 12% and 17%). The test solutions used to supply the sulphate ions and cations were 5%sodium sulphate solution. Compressive strengths measured on specimens were used to assess the changes in the mechanical properties of PET-mortars exposed to sulphate attack at different ages, mainly the Young modulus of elasticity. Based on experimental compressive tests on PETMortar composite specimens and there densities, the evolution of Young modulus of elasticity has been analyzed in accordance with normative models given by (ACI-318) and (BS-8110) codes of practice. In addition, a comparative study has been carried out for corrosion resistance coefficients K of unmodified mortar to those modified with waste PET particles. It can be noticed that, for the composite immersed in a corrosive Na2SO4 solution, the corrosion resistance coefficients decrease with the increase of the immersion period. The corrosion sulphate resistance K based on Young modulus before and after immersion of PET-mortar composites is better than that of the control mortar. Therefore, for safety considerations of PET-mortar composites use, ACI 318 is recommended code for design and investigation works. Also, it can be concluded that adding waste PET by volume fractions (6%, 12% and 17%) to blend Portland cement renders this cement more resistant to the sodium sulphate aggressive medium. Therefore, composites materials based waste PET aare often presented as the materials of the future because of their potential for innovation and the advantages they offer. In fact, using waste PET as cement substitutes reduces the energy consumption. These modified mortars address problems related to environmental pollution by CO2 emissions, and are used to repair various reinforced concrete structures in sodium sulphate aggressive mediums