Multi-agent market equilibria: mathematical models and empirical analyses

This thesis examines the framework of multi-agent market equilibria through math- ematical models and empirical analyses. Chapter 2 considers a model for the interaction between a slow institutional investor and a high- frequency trader by means of a stochastic multi-period Stack- elberg game. We determine the unique multi-period Stackelberg equilibrium of the game in terms of the resolvent of a Fredholm integral equation. Our results provide an explicit solution which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the trade-off be- tween the order-flow and the trading signal. We also show that the institutional investor’s strategy is more profitable when the order-flow of the high-frequency trader is taken into account. In Chapter 3 we study a model for a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. We prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. A comparison with the corre- sponding open-loop Nash equilibrium shows that both the agents’ optimal trading rates and their performance move towards the central-planner solution, since ex- cessive trading due to lack of coordination is reduced. Nevertheless, we find that the size of this effect is modest for plausible parameter values. Chapter 4 develops a methodology which accurately replicates the FTSE Rus- sell indexes reconstruction, including the quarterly rebalancings due to new initial public offerings (IPOs). We apply our index reconstruction protocol to compute the permanent and temporary price impact on the Russell 3000 annual additions and deletions, and on the quarterly additions of new IPOs. Our findings show that the index portfolios following the Russell 3000 index and rebalanced on an annual basis are overall more crowded than those following the index on a quarterly basis.Open Acces

Temporal Planning with Intermediate Conditions and Effects

Automated temporal planning is the technology of choice when controlling systems that can execute more actions in parallel and when temporal constraints, such as deadlines, are needed in the model. One limitation of several action-based planning systems is that actions are modeled as intervals having conditions and effects only at the extremes and as invariants, but no conditions nor effects can be specified at arbitrary points or sub-intervals. In this paper, we address this limitation by providing an effective heuristic-search technique for temporal planning, allowing the definition of actions with conditions and effects at any arbitrary time within the action duration. We experimentally demonstrate that our approach is far better than standard encodings in PDDL 2.1 and is competitive with other approaches that can (directly or indirectly) represent intermediate action conditions or effects

Evidence of Crowding on Russell 3000 Reconstitution Events

We develop a methodology which replicates in great accuracy the FTSE Russell indexes reconstitutions, including the quarterly rebalancings due to new initial public offerings (IPOs). While using only data available in the CRSP US Stock database for our index reconstruction, we demonstrate the accuracy of this methodology by comparing it to the original Russell US indexes for the time period between 1989 to 2019. A python package that generates the replicated indexes is also provided. As an application, we use our index reconstruction protocol to compute the permanent and temporary price impact on the Russell 3000 annual additions and deletions, and on the quarterly additions of new IPOs . We find that the index portfolios following the Russell 3000 index and rebalanced on an annual basis are overall more crowded than those following the index on a quarterly basis. This phenomenon implies that transaction costs of indexing strategies could be significantly reduced by buying new IPOs additions in proximity to quarterly rebalance dates.Comment: 34 pages, 9 figure

Formal Analysis and Verification of Max-Plus Linear Systems

Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of MPL, taking into account both structural properties such as transient and cyclicity, and the open problem of user-defined temporal properties. We propose Time-Difference LTL (TDLTL), a logic that encompasses the delays between the discrete time events governed by an MPL system, and characterize the problem of model checking TDLTL over MPL. We first consider a framework based on the verification of infinite-state transition systems, and propose an approach based on an encoding into model checking. Then, we leverage the specific features of MPL systems to devise a highly optimized, combinational approach based on Satisfiability Modulo Theory (SMT). We experimentally evaluate the features of the proposed approaches on a large set of benchmarks. The results show that the proposed approach substantially outperforms the state of the art competitors in expressiveness and effectiveness, and demonstrate the superiority of the combinational approach over the reduction to model checking.Comment: 28 pages (including appendixes

Compositional generative mapping for tree-structured data - Part II: Topographic projection model

We introduce GTM-SD (Generative Topographic Mapping for Structured Data), which is the first compositional generative model for topographic mapping of tree-structured data. GTM-SD exploits a scalable bottom-up hidden-tree Markov model that was introduced in Part I of this paper to achieve a recursive topographic mapping of hierarchical information. The proposed model allows efficient exploitation of contextual information from shared substructures by a recursive upward propagation on the tree structure which distributes substructure information across the topographic map. Compared to its noncompositional generative counterpart, GTM-SD is shown to allow the topographic mapping of the full sample tree, which includes a projection onto the lattice of all the distinct subtrees rooted in each of its nodes. Experimental results show that the continuous projection space generated by the smooth topographic mapping of GTM-SD yields a finer grained discrimination of the sample structures with respect to the state-of-the-art recursive neural network approach

Closed-Loop Nash Competition for Liquidity

We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central-planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values.Comment: 41 pages, 5 figures, supplementary appendi

The Varied Role of Efflux Pumps of the MFS Family in the Interplay of Bacteria with Animal and Plant Cells

Efflux pumps represent an important and large group of transporter proteins found in all organisms. The importance of efflux pumps resides in their ability to extrude a wide range of antibiotics, resulting in the emergence of multidrug resistance in many bacteria. Besides antibiotics, multidrug efflux pumps can also extrude a large variety of compounds: Bacterial metabolites, plant-produced compounds, quorum-sensing molecules, and virulence factors. This versatility makes efflux pumps relevant players in interactions not only with other bacteria, but also with plant or animal cells. The multidrug efflux pumps belonging to the major facilitator superfamily (MFS) are widely distributed in microbial genomes and exhibit a large spectrum of substrate specificities. Multidrug MFS efflux pumps are present either as single-component transporters or as tripartite complexes. In this review, we will summarize how the multidrug MFS efflux pumps contribute to the interplay between bacteria and targeted host cells, with emphasis on their role in bacterial virulence, in the colonization of plant and animal host cells and in biofilm formation. We will also address the complexity of these interactions in the light of the underlying regulatory networks required for the effective activation of efflux pump genes

Evidence for a quadruplex structure in the polymorphic hs1.2 enhancer of the immunoglobulin heavy chain 3’ regulatory regions and its conservation in mammals

Regulatory regions in the genome can act through a variety of mechanisms that range from the occurrence of histone modifications to the presence of protein-binding loci for self-annealing sequences. The final result is often the induction of a conformational change of the DNA double helix, which alters the accessibility of a region to transcription factors and consequently gene expression. A similar to 300 kb regulatory region on chromosome 14 at the 3' end (3'RR) of immunoglobulin (Ig) heavy-chain genes shows very peculiar features, conserved in mammals, including enhancers and transcription factor binding sites. In primates, the 3'RR is present in two copies, both having a central enhancer named hs1.2. We previously demonstrated the association between different hs1.2 alleles and Ig plasma levels in immunopathology. Here, we present the analysis of a putative G-quadruplex structure (tetraplex) consensus site embedded in a variable number tandem repeat (one to four copies) of hs1.2 that is a distinctive element among the enhancer alleles, and an investigation of its three-dimensional structure using bioinformatics and spectroscopic approaches. We suggest that both the role of the enhancer and the alternative effect of the hs1.2 alleles may be achieved through their peculiar three-dimensional-conformational rearrangement

TRF1 and TRF2 binding to telomeres is modulated by nucleosomal organization

The ends of eukaryotic chromosomes need to be protected from the activation of a DNA damage response that leads the cell to replicative senescence or apoptosis. In mammals, protection is accomplished by a six-factor complex named shelterin, which organizes the terminal TTAGGG repeats in a still ill-defined structure, the telomere. The stable interaction of shelterin with telomeres mainly depends on the binding of two of its components, TRF1 and TRF2, to double-stranded telomeric repeats. Tethering of TRF proteins to telomeres occurs in a chromatin environment characterized by a very compact nucleosomal organization. In this work we show that binding of TRF1 and TRF2 to telomeric sequences is modulated by the histone octamer. By means of in vitro models, we found that TRF2 binding is strongly hampered by the presence of telomeric nucleosomes, whereas TRF1 binds efficiently to telomeric DNA in a nucleosomal context and is able to remodel telomeric nucleosomal arrays. Our results indicate that the different behavior of TRF proteins partly depends on the interaction with histone tails of their divergent N-terminal domains. We propose that the interplay between the histone octamer and TRF proteins plays a role in the steps leading to telomere deprotection