In this short paper we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations. We derive this representation from a classical differentiability result for backward stochastic differential...

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...

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...

Regime switching is a well-known approach to incorporate significant changes in the modelling of financial data, like interest rates and default intensities. In the context of one of the standard pricing models, the CIR model with jumps, we analyse the effect of regime switching on the prices of...

In time series of financial data one often observes significant sudden changes as in the credit crisis in 2008. One way to model those changes is regime switching. Here we show how to handle regime switching in a tree associated with a Cox-Ingersoll-Ross short rate process

Values of tranche spreads of collateralized debt obligations (CDOs) are driven by the joint default performance of the assets in the collateral pool. The dependence between the names in the portfolio mainly depends on current economic conditions. Therefore, a correlation implied from tranches...