Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing, we provide a new approach to asset pricing based on Backward Volterra equations. The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs. We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which, to the best of our knowledge, has not yet been studied. We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations. Finally, we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.

中文翻译：

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连续时间夏普比率的期限结构与无套利资产定价

受金融和实证论点的启发，为了引入更灵活的定价方法，我们提供了一种基于 Backward Volterra 方程的资产定价新方法。该方法依赖于连续时间的无套利和不完全市场设置，通过根据评估时间或收益的到期选择非唯一定价措施。我们表明，在后一种情况下，动力学可以通过这里引入的延时后向随机沃尔泰拉积分方程来捕捉，据我们所知，该方程尚未被研究过。然后我们证明了时延后向随机沃尔泰拉积分方程的存在唯一性结果。最后，