RAPPORTI INTERNI 2006
Research Series
Title:  Pricing for geometric marked point processes under partial information: Entropy approach

Author(s):  Claudia Ceci and Anna Gerardi

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Tech.rep.number:  R2006007 
Abstract:  The problem of the arbitragefree pricing of a European contingent claim is considered in a general model for intraday stock price movements in the case of partial information. The dynamics of the risky asset price is described through a marked point process Y, whose local characteristics depend on some unobservable jump diffusion process X. The processes Y and X may have common jump times, which means that the trading activity may affect the law of X and could be also related to the presence of catastrophic events. Riskneutral measures are characterized. In particular, the minimal entropy martingale measure is studied and the dynamic utility indifference price of the claim is introduced, providing a motivation for the approach chosen to deal with the problem of pricing under restricted information. 
Title:  Option Hedging for High Frequency Data Models

Author(s):  Claudia Ceci

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Tech.rep.number:  R2006006 
Abstract:  Hedging strategies for contingent claims are studied in a general model for high frequency data. The dynamics of the risky asset price is described through a marked point process Y, whose local characteristics depend on some hidden state variable X. The two processes Y and X may have common jump times, which means that the trading activity may affect the law of X and could be also related to the presence of catastrophic events. Since the market considered is incomplete one has to choose some approach to hedging derivatives. We choose the local riskminimization criterion. When the price of the risky asset is a general semimartingale, if an optimal strategy exists, the value of the portfolio is computed in the terms of the socalled minimal martingale measure and may be interpreted as a possible arbitragefree price. In the case where the price of the risky asset is modeled directly under a martingale measure, the computation of the riskminimizing hedging strategy is given. By using a projection result, we also obtain the riskminimizing hedging strategy under partial information when the hedger is restricted to observing only the past asset prices and not the exogenous process X which drives their dynamics. 
Title:  Metaheuristics for the Portfolio Selection Problem

Author(s):  Giacomo di Tollo and Andrea Roli

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Tech.rep.number:  R2006005 
Abstract:  The Portfolio selection problem is a relevant problem arising in finance and economics. While its basic formulation can be efficiently solved through linear programming, its more practical and realistic variants, that include various kinds of constraints and objectives, have to be tackled by approximate algorithms. Among the most effective approximate algorithms, are metaheuristic methods that have been proven to be very successful in many applications. This paper presents an overview of the main formulations of the Portfolio selection problem and surveys the literature on the application of metaheuristics to it.

Title:  HIV evolution according to a thirteen immunologicalclinical state model: a semiMarkov approach

Author(s):  Giuseppe Di Biase and Arturo Di Girolamo and Jacques Janssen and Stefano Iacobelli and Nicola Tinari and Raimondo Manca

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Tech.rep.number:  R2006004 
Abstract:  In the paper an analysis of HIV/AIDS dynamics, defined by clinical and immunological gravity levels, according to Centre Disease Control guidelines, has been made by means of homogeneous semiMarkov stochastic processes. The clinicalimmunological aspects defining the states considered are related to patient symptomatology and to CD4 lymphocytes count. Many results useful to a health decision maker have been obtained. They include: the conditional probabilities that a infected patient will be in state j after a time t given that she/he entered at time 0 (starting time) in the state i; that she/he will survive until a time t, given the starting state; that she/he will keep on staying in the starting state until time t; that she/he will get to stage j of the disease at the next transition, if the previous state was i and no state change occurred up to the time t. Data set refer to subjects selected from a series of 766 HIVpositive intravenous drug users.

Title:  A Stochastic Model for the HIV/AIDS Dynamic Evolution

Author(s):  Giuseppe Di Biase and Guglielmo D'Amico and Arturo Di Girolamo and Jacques Janssen and Stefano Iacobelli and Nicola Tinari and Raimondo Manca

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Tech.rep.number:  R2006003 
Abstract:  In the paper an analysis of HIV/AIDS dynamics, defined by CD4 levels, has been made from a macroscopic point of view by means of homogeneous semiMarkov stochastic processes. Many results have been obtained. They include the following conditional probabilities: that a infected patient will be in state j after a time t given that she/he entered at time 0 (starting time) in the state i; that she/he will survive until a time t, given the starting state; that she/he will keep on staying in the starting state until time t; that she/he will get to stage j of the disease at the next transition, if the previous state was i and no state change occurred up to the time t. Finally the average patient cost until time t, given the starting state, has been computed. The immunological states considered are related to CD4 counts and our data refer to subjects selected from a series of 766 HIVpositive intravenous drug users.

Title:  Portfolio Selection Problem by Metaheuristics: An Annotated Bibliography.

Author(s):  Giacomo di Tollo

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Tech.rep.number:  R2006002 
Abstract:  Portfolio Selection Problem (PSP) is one of the most studied issues in finance: It is concerned with selecting the portfolio of assets which minimize the risk given a certain level of returns. The PSP belongs to the class of combinatorial optimization problems and adding constraints to the basic formulation lead the problem to be NPHard, so metaheuristic approaches can be succesfully applied to solve the problem. This work is aimed in developing a conceptual analysis about Metaheuristic approaches developed in literature to this extent, introducing the problem, classifying the general concepts and outlining the most used strategies.

Title:  Filling knapsacks wirh candies, Integer Linear Programming in Fair Division

Author(s):  Marco Dall'Aglio and Raffaele Mosca

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Tech.rep.number:  R2006001 
Abstract:  We consider the problem of allocating a finite number of indivisible items to two players. The search for a minimax allocation can be formulated as an Integer Linear Programming (ILP) problem, carrying some similarities with the 01 knapsack problem. Typical tools of integer programming, such as dynamic programming or the branch and bound algorithm can be successfully adapted to design new procedures in fair division.

