  In a Markovian stochastic volatility model, we consider financial agents
whose investment criteria are modelled by forward exponential performance
processes. The problem of contingent claim indifference valuation is first
addressed and a number of properties are proved and discussed. Special
attention is given to the comparison between the forward exponential and the
backward exponential utility indifference valuation. In addition, we construct
the problem of optimal risk sharing in this forward setting and solve it when
the agents' forward performance criteria are exponential.
