Real Time Linear Scheduling
Algo trading, and specifically high frequency trading is a highly competitive discipline in which we are presented with both theoretical and technological challenges. While we want our algorithm to make the best possible decision at any point in time, it must also react to an online stream of events. Assume at time T we may execute any of N “buy” orders in different stocks s1, , sN. Let vi(T+t) be the value function of the i-th order sent at time T+t. We assume that the vi’s are decreasing functions of time, however they might differ from one another.
Furthermore, we know that by delaying our decision to act, another player may beat us and send an order of their own. Thus, a scheduling problem arises naturally as we create a stack of our orders.
In this lecture we present a solution that on the one hand gives an approximated solution to the ordering and on the other, addresses the necessity to perform quick in short time scale.