Dynamically complete markets under Brownian motion

This paper investigates how continuous-time trading renders complete a financial market in which the underlying risk process is a Brownian motion. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, has been established in the literature for single-commodity, pure-exchange economies with many heterogenous agents where the securities’ dividends as well as the agents’ utilities and endowments include flows during the trading horizon which are analytic functions. In sharp contrast, the present analysis is based upon a different mathematical argument that assumes neither analyticity nor a particular underlying economic environment. The novelty of our approach lies in deriving closed-form expressions for the dispersion coefficients of the securities’ prices. To this end, we assume only that the pricing kernels and dividends satisfy standard growth and smoothness restrictions (mild enough to allow even for options). In this sense, our sufficiency conditions apply irrespectively of preferences, endowments or other structural elements (for instance, whether or not the budget constraints include only pure exchange).

Compacting oblivious agents on dynamic rings

In this paper we investigate dynamic networks populated by autonomous mobile agents. Dynamic networks are networks whose topology can change continuously, at unpredictable locations and at unpredictable times. These changes are not considered to be faults, but rather an integral part of the nature of the system. The agents can autonomously move on the network, with the goal of solving cooperatively an assigned common task. Here, we focus on a specific network: the unoriented ring. More specifically, we study 1-interval connected dynamic rings (i.e., at any time, at most one of the edges might be missing). The agents move according to the widely used Look–Compute–Move life cycle, and can be homogenous (thus identical) or heterogenous (agents are assigned colors from a set of c > 1 colors). For identical agents, their goal is to form a compact segment, where agents occupy a continuous part of the ring and no two agents occupy the same node: we call this the Compact Configuration Problem. In the case of agents with colors, called the Colored Compact Configuration Problem, the goal is to group agents such that each group is formed by all agents having the same color, it occupies a continuous segment of the network, and groups of agents having different colors occupy distinct areas of the network. In this paper we determine the necessary conditions to solve both proposed problems. For all solvable cases, we provide algorithms for both the monochromatic and the colored version of the compact configuration problem. All our algorithms work even for the simplest model where agents have no persistent memory, no communication capabilities and do not agree on a common orientation within the network. To the best of our knowledge this is the first work on the compaction problem in a dynamic network.

Assemblages in the Venetian Lagoon: Humans, water and multiple historical flows

Since the dawn of its existence, and at times thanks to ambitious interventions, Venice and its lagoon have needed to be constantly protected from the various ways in which water has reclaimed its existence. This article asserts that the ways in which Venice approached the watery world imply a tendency to relate to the natural environment as if it was something humans ought to separate themselves from, rather than something towards which they could harmoniously relate. As a result of this mindset, the natural changes which made humans interventions necessary are most often phrased as events abruptly sprouted into being, and less as obvious consequences of pre-existing ecological alterations of the islands’ ecosystem throughout the centuries. In order to read these events differently, this article adopts assemblage theory as delineated in the work of Manuel DeLanda (2006], 2016), according to which history comprises a multiplicity of flows, each belonging to a specific social reality. As such, this article auspicates a way to read ecological alterations of the Venetian lagoon beyond the mere actions of humans and to see, instead, socio-natural changes as the result of intricate relations between heterogenous agents and forces.