We consider central bank strategies for maintaining a currency peg through the generation of price impact. While the central bank can in principle create unlimited amounts of the domestic currency, any such strategy will lead to the aggregation of an ever-increasing risky position in foreign reserves. In a first step, we solve for an intervention strategy that, for the case of a one-sided currency peg, minimizes the foreign currency reserves in a pathwise manner. In the next step, we add to this model a large speculator, whose aim is to break the currency peg. This leads to a system of two coupled singular control problems, for which we establish a Stackelberg equilibrium. We also discuss central bank strategies with slippage for two-sided currency pegs. This talk is based on joint work with Eyal Neuman, Chengguo Weng, and Xiaole Xue.
Short bio: Alexander Schied is a Professor and University Research Chair in the Department of Statistics and Actuarial Science at the University of Waterloo. His research is in probability theory and stochastic analysis with applications to mathematical finance and economics. Recent research topics include risk measurement and risk management, modelling and optimization in finance and economics, robustness and model uncertainty, and issues arising from market microstructure and price impact. Together with Hans Föllmer he co-authored the book Stochastic Finance: An Introduction in Discrete Time. Alexander Schied is currently Co-Editor of the journal Finance and Stochastics and member of several other editorial boards, including Applied Mathematics and Optimization, Mathematical Finance, the SIAM Journal on Financial Mathematics, and the SIAM Book Series on Financial Mathematics. He holds a doctoral degree in mathematics from the University of Bonn.