In this paper, we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations (BSDEs). We derive this representation from a classical differentiability result for BSDEs and the full allocation...

In a recent paper, Soner, Touzi and Zhang (2012) [19] have introduced a notion of second order backward stochastic differential equations (2BSDEs), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in...

The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related credit valuation adjustment (CVA), debt valuation adjustment (DVA), liquidity valuation adjustment (LVA) and replacement cost (RC) issues,...

Under the most elementary conditions on stochastic differential equations and some milder conditions on backward stochastic differential equations with finite or infinite time intervals and linear-growth generators, a representation theorem of generators and a converse comparison theorem of...

In this paper, the existence of Lp(p>1) solutions for one-dimensional backward stochastic differential equations will be shown directly by proving that an approximation sequence is a Cauchy one in the Lp sense.