Recent empirical studies suggest a downward sloping term structure of Sharpe ratios. We present a theoretical framework in continuous time that can cope with such a non-flat forward curve of risk prices. The approach departs from an arbitrage-free and incomplete market setting when different pricing measures are possible. Involved pricing measures now depend on the time of evaluation or the maturity of payoffs. This results in a time inconsistent pricing scheme. The dynamics can be captured by a time-delayed backward stochastic Volterra integral equation, which to the best of our knowledge, has not yet been studied.
term structures sharpe ratio incomplete markets asset pricing time inconsistency arbitrage (time-delayed) volterra equations