Paolo Pra | Università degli Studi di Padova (original) (raw)

Papers by Paolo Pra

SSRN Electronic Journal, 2000

In this paper we propose a simple binary mean field game, where N agents may decide whether to tr... more In this paper we propose a simple binary mean field game, where N agents may decide whether to trade or not a share of a risky asset in a liquid market. The asset's returns are endogenously determined taking into account demand and transaction costs. Agents' utility depends on the aggregate demand, which is determined by all agents' observed and forecasted actions. Agents are boundedly rational in the sense that they can go wrong choosing their optimal strategy. The explicit dependence on past actions generates endogenous dynamics of the system. We, firstly, study under a rather general setting (risk attitudes, pricing rules and noises) the aggregate demand for the asset, the emerging returns and the structure of the equilibria of the asymptotic game. It is shown that multiple Nash equilibria may arise. Stability conditions are characterized, in particular boom and crash cycles are detected. Then we precisely analyze properties of equilibria under significant examples, performing comparative statics exercises and showing the stabilizing property of exogenous transaction costs.

Annales De L Institut Henri Poincare-probabilites Et Statistiques - ANN INST HENRI POINCARE-PROB, 2000

We obtain sharp asymptotics for the first time a “macroscopic” density fluctuation occurs in a sy... more We obtain sharp asymptotics for the first time a “macroscopic” density fluctuation occurs in a system of independent simple symmetric random walks on Zd. Also, we show the convergence of the moments of the rescaled time by establishing tail estimates.

Stochastic Processes and their Applications, 2009

We study the impact of contagion in a network of firms facing credit risk. We describe an intensi... more We study the impact of contagion in a network of firms facing credit risk. We describe an intensity based model where the homogeneity assumption is broken by introducing a random environment that makes it possible to take into account the idiosyncratic characteristics of the firms. We shall see that our model goes behind the identification of groups of firms that can be considered basically exchangeable. Despite this heterogeneity assumption our model has the advantage of being totally tractable. The aim is to quantify the losses that a bank may suffer in a large credit portfolio. Relying on a large deviation principle on the trajectory space of the process, we state a suitable law of large number and a central limit theorem useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.

Stochastic Processes and Their Applications, 2010

The use of Markov chains in simulation has raised a number of questions concerning qualitative an... more The use of Markov chains in simulation has raised a number of questions concerning qualitative and quantitative features of random processes, in particular in connection with mixing properties. Among the features that are useful in the analysis of effectiveness of Markov ...

Annals of Probability - ANN PROBAB, 2001

We study quasi-stationary measures for conservative particle systems in the in finite lattice. Ex... more We study quasi-stationary measures for conservative particle systems in the in finite lattice. Existence of quasi-stationary measures is established for a fairly general class of reversible systems. For the special cases of a system of independent random walks and the symmetric simple exclusion process, it is shown that qualitative features of quasi-stationary measures change drastically with dimension.

Mathematics of Control, Signals, and Systems (MCSS), 2003

The scalar di¤erential inclusion

Mathematics of Control, Signals, and Systems, 1996

We consider duality relations between risk-sensitive stochastic control problems and dynamic game... more We consider duality relations between risk-sensitive stochastic control problems and dynamic games. They are derived from two basic duality results, the first involving free energy and relative entropy and resulting from a Legendre-type transformation, the second involving power functions. Our approach allows us to treat, in essentially the same way, continuous-and discrete-time problems, with complete and partial state observation, and leads to a very natural formal justification of the structure of the cost functional of the dual. It also allows us to obtain the solution of a stochastic game problem by solving a risk-sensitive control problem.

Mathematical Methods of Operations Research, 1997

ABSTRACT We study the applicability of the method of Dynamic Programming (DP) for the solution of... more ABSTRACT We study the applicability of the method of Dynamic Programming (DP) for the solution of a general class of sequential decision problems under uncertainty, that may more commonly be referred to as discrete-time control problems under uncertainty. The uncertainty is due to the fact that the evolution of the state of the controlled system is affected by disturbances that are only known to belong to random sets, whose distributions are given a-priori. This includes as special cases the well known stochastic control problem and the robust min-max problem.

Journal of Statistical Physics, 1996

We apply large-deviation theory to particle systems with a random mean-field interaction in the M... more We apply large-deviation theory to particle systems with a random mean-field interaction in the McKean-Vlasov limit. In particular, we describe large deviations and normal fluctuations around the McKean-Vlasov equation. Due to the randomness in the interaction, the McKean-Vlasov equation is a collection of coupled PDEs indexed by the state space of the single components in the medium. As a result, the study of its solution and of the finite-size fluctuation around this solution requires some new ingredient as compared to existing techniques for nonrandom interaction.

Journal of Functional Analysis, 2006

We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a ... more We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasaki-type dynamics in the lattice without exclusion, and in the continuum. New estimates for Glauber-type dynamics are also obtained.

Bulletin of Mathematical Biology, 2006

The activation, growth and death of animal cells are accompanied by changes in the chemical compo... more The activation, growth and death of animal cells are accompanied by changes in the chemical composition of the surrounding environment. Cells and their microscopic environment constitute therefore a cellular ecosystem whose time-evolution determines processes of interest for either biology (e.g. animal development) and medicine (e.g. tumor spreading, immune response). In this paper, we consider a general stochastic model of the interplay between cells and environmental cellular niches. Niches may be either favourable or unfavourable in sustaining cell activation, growth and death, the state of the niches depending on the state of the cells. Under the hypothesis of random coupling between the state of the environmental niche and the state of the cell, the rescaled model reduces to a set of four non-linear differential equations. The biological meaning of the model is studied and illustrated by fitting experimental data on the growth of multicellular tumor spheroids. A detailed analysis of the stochastic model, of its deterministic limit, and of normal fluctuations is provided.

We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-... more We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time. To cite this article: P. Dai Pra et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). Résumé Monotonie et monotonie complète des chaînes de Markov à temps continu. Nous étudions les notions de monotonie et de monotonie complète pour les processus de Markov (ou chaînes de Markov à temps continu) prenant leurs valeurs dans un espace partiellement ordonné. Ces deux notions ne sont pas équivalentes, comme c'est le cas lorsque le temps est discret. Cependant, nous établissons que pour certains ensembles partiellement ordonnés, l'équivalence a lieu en temps continu bien que n'étant pas vraie en temps discret. Pour citer cet article : P. Dai Pra et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).

We consider a system of urns of Polya-type, with balls of two colors; the reinforcement of each u... more We consider a system of urns of Polya-type, with balls of two colors; the reinforcement of each urn depends both on the content of the same urn and on the average content of all urns. We show that the urns synchronize almost surely, in the sense that the fraction of balls of a given color converges almost surely, as the time goes to infinity, to the same limit for all urns. A normal approximation for a large number of urns is also obtained. *