This paper studies the moments and the distribution of the aggregate discounted claims (ADCs) in a Markovian environment, where the claim arrivals, claim amounts, and forces of interest (for discounting) are influenced by an underlying Markov process. Specifically, we assume that claims occur...

We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the solution of a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, and...

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven mechanism to construct low dimensional surrogate models. These...