Minimal supersolutions of convex BSDEs

We study the nonlinear operator of mapping the terminal value $\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower semicontinuous and bounded below by an affine function of the control variable $z$. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.Comment: Published in at http://dx.doi.org/10.1214/13-AOP834 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Group Level Swiss Solvency Test

In this paper we elaborate on Swiss Solvency Test (SST) consistent group diversification effects via optimizing the web of capital and risk transfer (CRT) instruments between the legal entities. A group level SST principle states that subsidiaries can be sold by the parent company at their economic value minus some minimum capital requirement. In a numerical example we examine the dependence of the optimal CRT on this minimum capital requirement. Our findings raise the question of how to actually implement this group level SST principle and how to define the respective level of minimum capital requirements, in particular.convex optimization; group diversification; minimum capital requirement; Swiss solvency test