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首页> 外文期刊>International journal of stochastic analysis >Optimal Foreign Exchange Rate Intervention in Lévy Markets
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Optimal Foreign Exchange Rate Intervention in Lévy Markets

机译:Lévy市场中的最佳汇率干预

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This paper considers an exchange rate problem in Lévy markets, where the Central Bank has to intervene.We assume that, in the absence of control, the exchange rate evolves according to Brownianmotionwith a jump component.TheCentral Bank is allowed to intervene in order to keep the exchange rate as close as possible to a prespecified target value.The interventions by the Central Bank are associated with costs.We present the situation as an impulse control problem, where the objective of the bank is to minimize the intervention costs. In particular, the paper extends themodel byHuang, 2009, to incorporate a jump component.We formulate and prove an optimal verification theorem for the impulse control.We then propose an impulse control and construct a value function and then verify that they solve the quasivariational inequalities. Our results suggest that if the expected number of jumps is high the Central Bank will intervene more frequently and with large intervention amounts hence the intervention costs will be high.
机译:本文考虑了中央银行必须干预的Lévy市场中的汇率问题。我们假设,在缺乏控制的情况下,汇率根据Brownianmotion的变化而具有跳跃成分,因此允许中央银行进行干预以保持利率不变。中央银行的干预措施与成本相关。我们将这种情况视为一种冲动控制问题,该银行的目标是将干预成本降至最低。尤其是本文对Huang(2009)的模型进行了扩展,加入了一个跳跃分量。我们制定并证明了脉冲控制的最优验证定理,然后提出了脉冲控制并构造了一个值函数,然后证明它们可以解决拟变分不等式。 。我们的结果表明,如果预期的跳高次数很高,则中央银行将更频繁地进行干预,并且干预量较大,因此干预成本将很高。

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