Details
Abstract: Algorithmic execution of large transactions in equity and other markets is a large and growing business. The goal is to optimize the overall execution results relative to some benchmark specified by the client, generally involving some combination of minimum market impact and exposure to volatilty risk. An increasingly important trend in recent years is dynamically adaptive algorithms, that adjust execution in response to short-term variations in estimated market liquidity and volatility. The mathematical challenge is to combine that instantaneous response with a more strategic point of view that optimizes an overall combination of impact cost and volatility risk. We summarize some recent work using dynamic programming to calculate and implement optimally adaptive strategies.