<p style='text-indent:20px;'>This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward stochastic differential equations with jumps (FBSDEJs, for short), we derive two systems of integro-partial differential equations (IPDEs, for short). Then, we rigorously prove a verification theorem which provides a sufficient condition for open-loop equilibrium strategies. As special cases, a mean-variance portfolio selection problem and a time-inconsistent problem under non-exponential discounting are discussed.</p>

中文翻译：

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一类时间不一致随机最优控制问题的开环平衡

<p style='text-indent:20px;'>本文研究了具有确定性系数的跳跃扩散SDE下一类一般时间不一致随机控制问题的开环均衡。受跳跃的前向后向随机微分方程（简称 FBSDEJs）的四步方案思想的启发，我们推导出了两个积分偏微分方程组（简称 IPDEs）。然后，我们严格证明了一个验证定理，它为开环均衡策略提供了充分条件。作为特例，讨论了非指数贴现下的均方差投资组合选择问题和时间不一致问题。</p>