Stochastic approximations and differential inclusions II: applications

We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaim, Hofbauer and Sorin (2005) to several adaptive processes used in game theory including: classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift is derived through a systematic application of the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size

Mean-Field Limits Beyond Ordinary Differential Equations

16th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2016, Bertinoro, Italy, June 20-24, 2016, Advanced LecturesInternational audienceWe study the limiting behaviour of stochastic models of populations of interacting agents, as the number of agents goes to infinity. Classical mean-field results have established that this limiting behaviour is described by an ordinary differential equation (ODE) under two conditions: (1) that the dynamics is smooth; and (2) that the population is composed of a finite number of homogeneous sub-populations, each containing a large number of agents. This paper reviews recent work showing what happens if these conditions do not hold. In these cases, it is still possible to exhibit a limiting regime at the price of replacing the ODE by a more complex dynamical system. In the case of non-smooth or uncertain dynamics, the limiting regime is given by a differential inclusion. In the case of multiple population scales, the ODE is replaced by a stochastic hybrid automaton

Crafting the Composite Garment: The role of hand weaving in digital creation

There is a growing body of practice-led textile research, focused on how digital technologies can inform new design and production strategies that challenge and extend the field. To date, this research has emphasized a traditional linear transition between hand and digital production; with hand production preceding digital as a means of acquiring the material and process knowledge required to negotiate technologies and conceptualize designs. This paper focuses on current Doctoral research into the design and prototyping of 3D woven or 'composite' garments and how the re-learning, or reinterpreting, of hand weaving techniques in a digital Jacquard format relies heavily on experiential knowledge of craft weaving skills. Drawing parallels between hand weaving and computer programming, that extend beyond their shared binary (pixel-based) language, the paper discusses how the machine-mediated experience of hand weaving can prime the weaver to ‘think digitally’ and make the transition to digital production. In a process where the weaver acts simultaneously as designer, constructor and programmer, the research explores the inspiring, but often indefinable space between craft and digital technology by challenging the notion that 'the relationship between hand, eye and material’ naturally precedes the use of computing (Harris 2012: 93). This is achieved through the development of an iterative working methodology that encompasses a cycle of transitional development, where hand weaving and digital processes take place in tandem, and techniques and skills are reinterpreted to exploit the advantages and constraints of each construction method. It is argued that the approach challenges the codes and conventions of computer programming, weaving and fashion design to offer a more sustainable clothing solution

After the sunset: the residual effect of temporary legislation

The difference between permanent legislation and temporary legislation is the default rule of termination: permanent legislation governs perpetually, while temporary legislation governs for a limited time. Recent literature on legislative timing rules considers the effect of temporary legislation to stop at the moment of expiration. When the law expires, so does its regulatory effect. This article extends that literature by examining the effect of temporary legislation beyond its expiration. We show that in addition to affecting compliance behavior which depends on statutory enforcement, temporary legislation also affects compliance behavior which does not depend on statutory enforcement, and more generally, organizational behavior after a sunset. When temporary legislation expires therefore, it can continue to administer regulatory and other effects. We specify the conditions for this process and give the optimal legislative response

Stochastic Approximation to Understand Simple Simulation Models

This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.Ministerio de Educación (JC2009- 00263), Ministerio de Ciencia e Innovación (CONSOLIDER-INGENIO 2010: CSD2010-00034, DPI2010-16920

Drug discovery for Chagas disease should consider Trypanosoma cruzi strain diversity.

This opinion piece presents an approach to standardisation of an important aspect of Chagas disease drug discovery and development: selecting Trypanosoma cruzi strains for in vitro screening. We discuss the rationale for strain selection representing T. cruzi diversity and provide recommendations on the preferred parasite stage for drug discovery, T. cruzi discrete typing units to include in the panel of strains and the number of strains/clones for primary screens and lead compounds. We also consider experimental approaches for in vitro drug assays. The Figure illustrates the current Chagas disease drug-discovery and development landscape