RAPPORTI INTERNI 2009
Research Series
Title:  Solving Weighted Argumentation Frameworks with Soft Constraints

Author(s):  Stefano Bistarelli and Daniele Pirolandi and Francesco Santini

Files: 
[pdf]
[bib]

Tech.rep.number:  R2009003 
Abstract:  We suggest soft constraints as a mean to parametrically represent and solve weighted Argumentation problems: different kinds of preference levels related to arguments, e.g. a score representing a fuzziness, a cost or a probability level of each argument, can be represented by choosing different semiring algebraic structures. The novel idea is to provide a common computational and quantitative framework where the computation of the classical Dung's extensions, e.g. the admissible extension, has an associated score representing "how much good" the set is. Preference values associated to arguments are clearly more informative and can be used to prefer a given set of arguments over others with the same characteristics (e.g. admissibility). Moreover, we propose a mapping from weighted Argumentation Frameworks to Soft Constraint Satisfaction Problems (SCSPs); with this mapping we can compute Dung semantics (e.g. admissible and stable) by solving the related SCSP. To implement this mapping we use JaCoP, a Java constraint solver.

Title:  Constraintbased Languages to model the Blood Coagulation Cascade

Author(s):  Stefano Bistarelli and Marco Bottalico and Francesco Santini

Files: 
[pdf]
[bib]

Tech.rep.number:  R2009002 
Abstract:  In this paper, we use different formal languages based on constraints to model biological reactions and use the blood coagulation cascade as a running example to analyze similarities and differences. Moreover we compare the results of the simulation with in vitro experiments in the medical scientific literature by also considering an hepatic inhibitor drug. Our study show how assets obtained with in vitro experiments could be modeled in silico using constraint languages.

Title:  Indifference valuation via Backward SDE's driven by Poisson martingales

Author(s):  Claudia Ceci

Files: 
[pdf]
[bib]

Tech.rep.number:  R2009001 
Abstract:  We prove the existence and uniqueness of bounded solutions to backward stochastic equations driven by two independent Poisson martingales in the case of locally Lipschitz generator having a certain monotonicity property. This result allows us to solve utility maximization problems with exponential preferences in an incomplete market where the risky asset dynamics is described by a pure jump process driven by two independent Poisson processes. This includes results on portfolio optimization under an additional European claim. Value processes of the optimal investment problems, optimal hedging strategies and the indifference price are represented in terms of solutions to BSDEs with generators satisfying the upper mentioned assumptions. Via a duality result, the solution to the dual problems are derived. In particular an explicit expression for the density of the minimal martingale measure is provided. The Markovian case is also discussed. This includes either asset dynamics dependent on a pure jump stochastic factor or claims written on a correlated nontradable asset.

