quant trading strategies - From a high frequency point of view, with a price prediction and assuming infinite leverage, how do you determine optimal trade size?

I have read about something like Kelly criterion for long term expectation maximization assuming a fixed starting bankroll. But if one can assume unlimited leverage, and one has a signal for a price movement..how could one go about deciding optimal trading sizes? It would seem to me like there are a lot of factors involved (things like transaction costs, inventories, etc..) - in practice would one come up with some intuitive model for this and run historical simulations for it? Or how would one tackle this? Is there any literature which I can read up on to understand this problem better?

Answer

There are few things to consider.

1. 
   

   Trading moves the price, to minimize market impact and maximize return it is generally optimal to split an order in several child orders. See the Kyle model.

   
   


2. 
   

   Splitting optimally dependents on specific assumptions that you make. The simplest (and first) approach is that of Berstsimas and Lo (Optimal Control of Execution Costs). Almagren improves on it considering more realistic price impact fuctions. You can find much of his work at his homepage. More recently, the focus has shifted to optimal submission strategies in the limit order book (e.g.: Obizhaeva and Wang) and to latency cost (for example see here).

   
   



3. 
   

   From a consistency perspective, the work of Jim Gatheral (No dynamic arbitrage and market costs) details some price impact functions that don't allow dynamic arbitrage (for example, "pump and dump" strategies). The high brow approach to these ideas is contained in the Econometrica paper by Stanzl and Huberman (Quasi-arbitrage and Price Manipulation). This area is expanding rapidly as several groups are working on expanding these results to limit order book markets.