Dynamic utility indifference valuation via convex risk measures

We study the dynamic utility indifference value process p(X) when the usefulness of X is evaluated via a dynamic monetary concave utility functional (DMCUF) instead of von Neumann/Morgenstern expected utility. A DMCUF is minus a dynamic convex risk measure. The key tools for our investigations are a representation of conditional convex risk measures (or MCUFs) and the convolution of abstract DMCUFs. We obtain conditions under which p( : ) is time-consistent and examine whether prices induced by p( : ) are consistent with the no-arbitrage principle. Since backward stochastic differential equations (BSDEs) induce timeconsistent DMCUFs, we also show how the valuation approach works in a BSDE setting.