Market-reaction-adjusted optimal central bank intervention policy in a forex market with jumps

Impulse control with random reaction periods (ICRRP) is used to derive a country’s optimal foreign exchange (forex) rate intervention policy when the forex market reacts to the interventions. This paper extends the previous work on ICRRP by incorporating a multi-dimensional jump diffusion process to model the state dynamics, and hence, enhance the viability of the extant model for applications. Furthermore, we employ a novel minimum cost operator that simplifies the computations of the optimal solutions. Finally, we demonstrate the efficacy of our framework by finding a market-reaction-adjusted optimal central bank intervention (CBI) policy for a country. Our numerical results suggests that market reactions and the jumps in the forex market are complements when the reactions increase the forex rate volatility; otherwise, they are substitutes.