Suppose that C = {cij : i, j ≥ 1} is a collection of i.i.d. nonnegative continuous random variables and suppose T is a rooted, directed tree on vertices labelled 1,2,. . . ,n. Then the ‘cost’ of T is defined to be c(T ) = ∑ (i,j)∈T cij , where (i, j) is denotes the directed edge from i to j in the tree T . Let Tn denote the ‘optimal’ tree, i.e. c(Tn) = min{c(T ) : T is a directed, rooted tree i...

We introduce an algorithm that generates an optimal controller for stochastic nonlinear problems with a periodic solution, e.g. locomotion. Uniquely, the quantity we approximate is neither the Value nor Policy functions, but rather the stationary statedistribution of the optimally-controlled process. We recast the control problem as Bayesian inference over a graphical model with a ring topology...

This paper presents a stochastic recursive procedure under constraints to find the optimal distance at which an agent must post his order to minimize his execution cost. We prove the a.s. convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are fulfilled (using notably principl...

The paper is concerned with a continuum model of the limit order book, viewed as a noncooperative game for n players. An external buyer asks for a random amount X > 0 of a given asset. This amount will be bought at the lowest available price, as long as the price does not exceed a given upper bound P . One or more sellers offer various quantities of the asset at different prices, competing to f...

Recent work on the design of monetary policy reflects a general consensus on the appropriate objectives of monetary policy. As articulated by Svensson, “....there is considerable agreement among academics and central bankers that the appropriate loss function both involves stabilizing inflation around an inflation target and stabilizing the real economy, represented by the output gap” (Lars E. ...

This paper studies four trading algorithms of a professional trader, in a realistic two-sided limit order book whose dynamics are driven by the order book events. The identity of the trader can be either privileged or regular, either a hedge fund or a brokery agency. The speed and cost of trading can be balanced by properly choosing active strategies on the displayed orders in the book and pass...

Methodology is presented for the design of single and double compressed limit Sequential Probability Ratio Tests (SPRT) and Cumulative Sum (CUSUM) control charts to detect one-sided mean shifts in a symmetric probability distribution. We also show how to evaluate the average run length properties with the Fast Initial Response (FIR) feature. The resulting CUSUM plans have a simple scoring proce...

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameter...

Aero-elastic systems, by their very nonlinear nature, frequently encounter Limit Cycle Oscillations (LCOs). An LCO occurs when the system being described reaches a periodic steady state where there is a constant exchange of energy between the various degrees of freedom, in this case: the Aero and Structural components. These LCOs might be benevolent at times, but are not so in most cases. In th...