Continuous-time regime-switching models are a very popular class of models for financial applications. In this work the so-called signal-to-noise matrix is introduced for hidden Markov models where the switching is driven by an unobservable Markov chain. Its relations to filtering, i.e. state...

We are concerned with the simulation and optimization of large-scale gas pipeline systems in an error-controlled environment. The gas flow dynamics is locally approximated by sufficiently accurate physical models taken from a hierarchy of decreasing complexity and varying over time. Feasible...

The proof of convergence of adaptive discretization-based algorithms for semi-infinite programs (SIPs) usually relies on compact host sets for the upper- and lower-level variables. This assumption is violated in some applications, and we show that indeed convergence problems can arise when...

A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision...

A recent paper by Schulze et al. (Math Methods Oper Res 92(1):107–132, 2020) presented the Rectangular Knapsack Problem ( Rkp ) as a crucial subproblem in the study on the Cardinality-constrained Bi-objective Knapsack Problem ( Cbkp ). To this end, they started an investigation into its...

Within a common arbitrage-free semimartingale financial market we consider the problem of determining all Nash equilibrium investment strategies for n agents who try to maximize the expected utility of their relative wealth. The utility function can be rather general here. Exploiting the...

We consider a portfolio optimization problem for a utility maximizing investor who is simultaneously restricted by convex constraints on portfolio allocation and upper and lower bounds on terminal wealth. After introducing a capped version of the Legendre–Fenchel-transformation, we use it to...

It is well known that linear prices supporting a competitive equilibrium exist in the case of convex markets, however, in the presence of integralities this is open and hard to decide in general. We present necessary and sufficient conditions for the existence of such prices for decentralized...