Capital allocations have been studied in conjunction with static risk measures in various papers. The dynamic case has been studied only in a discrete-time setting. We address the problem of allocating risk capital to subportfolios in a continuous-time dynamic context. For this purpose we...

The regime switching rough Heston model has two important features on different time scales. The regime switching is motivated by changes in the long term behaviour. The parameter of the model might change over time due to macro-economic reasons. Therefore we introduce a Markov chain to model...

We study existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs, in short) with jumps, where path-dependence means the dependence of the free term and generator of a path of a càdlàg process. Furthermore, we prove path-differentiability...

Archimedean copulae build a large family of copulae exhibiting tail-dependency in many cases. We extend the classical homogeneous (exchangeable) Archimedean copula to the heterogeneous case. This will extend the use of this copula family to multivariate random variable with pairwise different...

For the Markov property of a multivariate process, a necessary and sufficient condition on the multi-dimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends...