Optimal Trading Strategies in a Limit Order Market with Imperfect Liquidity

We study the optimal execution strategy of selling a security. In a continuous time diffusion framework, a risk-averse trader faces the choice of selling the security promptly or placing a limit order and hence delaying the transaction in order to sell at a more favorable price. We introduce a random delay parameter, which defers limit order execution and characterizes market liquidity. The distribution of expected time-to-fill of limit orders conforms to the empirically observed exponential distribution of trading times, and its variance decreases with liquidity. We obtain a closed-form solution and demonstrate that the presence of the lag factor linearizes the impact of other market parameters on the optimal limit price. Finally, two more stylized facts are rationalized in our model: the equilibrium bid-ask spread decreases with liquidity, but increases with agents risk aversion

On Heteropolymer Shape Dynamics

We investigate the time evolution of the heteropolymer model introduced by Iori, Marinari and Parisi to describe some of the features of protein folding mechanisms. We study how the (folded) shape of the chain evolves in time. We find that for short times the mean square distance (squared) between chain configurations evolves according to a power law, $D \sim t ^\nu$. We discuss the influence of the quenched disorder (represented by the randomness of the coupling constants in the Lennard-Jones potential) on value of the critical exponent. We find that $\nu$ decreases from $\frac{2}{3}$ to $\frac{1}{2}$ when the strength of the quenched disorder increases.Comment: 12 pages, very simple LaTeX file, 6 figures not included, sorry. SCCS 33

The Impact of Reduced Pre-Trade Transparency Regimes on Market Quality

This paper studies the effects of pre-trade quote transparency on spread, price discovery and liquidity in an artificial limit order market with heterogeneous trading rules. Our agent-based numerical experiments suggest that full quote transparency incurs substantial transaction costs to traders and dampens trading activity in an order-driven market. Our finding reveals that exogenous restriction of displayed depth, up to several best quotes, does not benefit market performance. On the contrary, endogenous restriction of displayed quote depth, by means of iceberg orders, improves market quality in multiple dimensions: it reduces average transaction costs, maintains higher liquidity and moderate volatility, balances the limit order book, and enhances price discovery

The Apparent Madness of Crowds: Irrational collective behavior emerging from interactions among rational agents

Standard economic theory assumes that agents in markets behave rationally. However, the observation of extremely large fluctuations in the price of financial assets that are not correlated to changes in their fundamental value, as well as the extreme instance of financial bubbles and crashes, imply that markets (at least occasionally) do display irrational behavior. In this paper, we briefly outline our recent work demonstrating that a market with interacting agents having bounded rationality can display price fluctuations that are {\em quantitatively} similar to those seen in real markets.Comment: 4 pages, 1 figure, to appear in Proceedings of International Workshop on "Econophysics of Stock Markets and Minority Games" (Econophys-Kolkata II), Feb 14-17, 200

A fitness model for the Italian Interbank Money Market

We use the theory of complex networks in order to quantitatively characterize the formation of communities in a particular financial market. The system is composed by different banks exchanging on a daily basis loans and debts of liquidity. Through topological analysis and by means of a model of network growth we can determine the formation of different group of banks characterized by different business strategy. The model based on Pareto's Law makes no use of growth or preferential attachment and it reproduces correctly all the various statistical properties of the system. We believe that this network modeling of the market could be an efficient way to evaluate the impact of different policies in the market of liquidity.Comment: 5 pages 5 figure

Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization

This paper addresses the parallel machine scheduling problem with family dependent setup times and total weighted completion time minimization. In this problem, when two jobs j and k are scheduled consecutively on the same machine, a setup time is performed between the finishing time of j and the starting time of k if and only if j and k belong to different families. The problem is strongly NP-hard and is commonly addressed in the literature by heuristic approaches and by branch-and-bound algorithms. Achieving proven optimal solution is a challenging task even for small size instances. Our contribution is to introduce five novel mixed integer linear programs based on concepts derived from one-commodity, arc-flow and set covering formulations. Numerical experiments on more than 13000 benchmark instances show that one of the arc-flow models and the set covering model are quite efficient, as they provide on average better solutions than state-of-the-art approaches, with shorter computation times, and solve to proven optimality a large number of open instances from the literature

A quantitative model of trading and price formation in financial markets

We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.Comment: 5 pages, 4 figure

A heuristic algorithm for a single vehicle static bike sharing rebalancing problem

The static bike rebalancing problem (SBRP) concerns the task of repositioning bikes among stations in self-service bike-sharing systems. This problem can be seen as a variant of the one-commodity pickup and delivery vehicle routing problem, where multiple visits are allowed to be performed at each station, i.e., the demand of a station is allowed to be split. Moreover, a vehicle may temporarily drop its load at a station, leaving it in excess or, alternatively, collect more bikes from a station (even all of them), thus leaving it in default. Both cases require further visits in order to meet the actual demands of such station. This paper deals with a particular case of the SBRP, in which only a single vehicle is available and the objective is to find a least-cost route that meets the demand of all stations and does not violate the minimum (zero) and maximum (vehicle capacity) load limits along the tour. Therefore, the number of bikes to be collected or delivered at each station must be appropriately determined in order to respect such constraints. We propose an iterated local search (ILS) based heuristic to solve the problem. The ILS algorithm was tested on 980 benchmark instances from the literature and the results obtained are competitive when compared to other existing methods. Moreover, our heuristic was capable of finding most of the known optimal solutions and also of improving the results on a number of open instances

Hamiltonian dynamics of homopolymer chain models

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the theta-transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.Comment: 11 pages, 8 figures, accepted for publication in Physical Review

Delineation of the Native Basin in Continuum Models of Proteins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield the similar results. As a byproduct, a simple method to determine the folding temperature is obtained.Comment: REVTeX, 6 pages, 5 EPS figure