We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever-increasing risky position in foreign reserves. We describe this situation mathematically by means of two coupled singular control problems, where the common singularity arises from a local time along a random curve. Our first result identifies a certain local time as that central bank strategy for which this risk position is minimized. We then consider the worst-case situation the central bank may face by identifying that strategy of the strategic investor that maximizes the expected inventory of the central bank under a cost criterion, thus establishing a Stackelberg equilibrium in our model.

中文翻译：

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保护挂钩货币市场免受投机投资者的影响

我们考虑在目标区域市场中交易者和中央银行之间的随机博弈，货币挂钩较低。这种货币挂钩由中央银行通过产生永久性价格影响来维持，从而使外汇储备中的风险头寸不断增加。我们通过两个耦合奇异控制问题在数学上描述了这种情况，其中公共奇异点来自沿随机曲线的本地时间。我们的第一个结果将某个当地时间确定为该风险头寸最小化的中央银行策略。然后，我们通过确定战略投资者在成本标准下最大化中央银行预期库存的策略来考虑中央银行可能面临的最坏情况，从而在我们的模型中建立斯塔克伯格均衡。