不确定投资中期望收益和期望成本收益的最优停时
Optimal stopping of expected profit and cost yields in an investment under uncertainty
摘要：
研究了不确定性条件下投资的期望利润和成本现金流之间的权衡策略的有限时域最优停时问题。最优问题首先制定在一个系统的Snell信封的利润和成本收益率作为障碍。然后，我们构造一个最小和最大的解决方案，使用的相关系统的反射向后的SDES的近似计划。当现金流的不确定性的来源，如波动的市场价格，假设根据扩散过程演变的依赖，是明确的，我们也得到了这些解决方案和粘性解决方案的变分不等式（VI）与互联障碍系统之间的连接。我们还提供了两个反例，说明（VI）的解的唯一性一般不成立。
英文摘要：
We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We then construct both a minimal and a maximal solutions using an approximation scheme of the associated system of reflected backward SDEs. When the dependence of the cash-flows on the sources of uncertainty, such as fluctuation market prices, assumed to evolve according to a diffusion process, is made explicit, we also obtain a connection between these solutions and viscosity solutions of a system of variational inequalities (VI) with interconnected obstacles. We also provide two counter-examples showing that uniqueness of solutions of (VI) does not hold in general.
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