We prove an anticipative sufficient stochastic minimum principle in a jump process setup with initially enlarged filtrations. We apply the result to several portfolio selection problems like mean and minimal variance hedging under enlarged filtrations. We also investigate utility maximizing portfolio selection under future information. Contrarily to classical optimization methods like dynamic programing, our stochastic minimum principle likewise applies to non-Markovian setups. On the mathematical side, we are concerned with jump processes, forward and backward stochastic differential equations and forward integrals.

中文翻译：

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扩大过滤条件下的预期随机最小原理

我们证明了在初始放大过滤的跳跃过程设置中预期的足够随机最小原理。我们将结果应用于多个投资组合选择问题，例如扩大过滤条件下的均值和最小方差对冲。我们还将研究在未来信息下最大化选择投资组合的效用。与经典的优化方法（例如动态编程）相反，我们的随机最小原理同样适用于非马尔可夫设置。在数学方面，我们关注跳跃过程，前向和后向随机微分方程和前向积分。