Optimal trade execution: A mean quadratic variation approach

A Hamilton Jacobi Bellman Approach to Optimal Trade Execution

The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a Linear-Quadratic (LQ) optimal stochastic control problem, A semi-Lagrangian scheme is used to solve the resulting non-linear Hamilton Jacobi Bellman (HJB) PDE. This method is essentially independent of the form for the price impact f...

Mean-Variance Optimal Adaptive Execution

Electronic trading of equities and other securities makes heavy use of “arrival price” algorithms, that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean-variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substant...

Dynamic trade execution: a grammatical evolution approach

Trade execution is concerned with the actual mechanics of buying or selling the desired amount of a financial instrument. Investors wishing to execute large orders face a tradeoff between market impact and opportunity cost. Trade execution strategies are designed to balance out these costs, thereby minimising total trading cost. Despite the importance of optimising the trade execution process, ...

Optimal Trade Execution in Illiquid Markets

We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the order flow N is given by a Poisson process, we give a full analysis of the properties and computation of the optimal dynamic execution strategy. Extensions, w...

Optimal trade execution of equities in a limit order market