Giovanni Paolo Crespi | Università Carlo Cattaneo - LIUC (original) (raw)

Papers by Giovanni Paolo Crespi

Research paper thumbnail of Pointwise and global well-posedness in set optimization: a direct approach

Annals of Operations Research, 2017

The aim of this paper is to characterize some of the pointwise and global wellposedness notions a... more The aim of this paper is to characterize some of the pointwise and global wellposedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.

Research paper thumbnail of Is it safe to play it safe

The future has yet to come but you have a right to shape it. We test empirical data on European I... more The future has yet to come but you have a right to shape it. We test empirical data on European IRS market to check the truthfulness of this sentence. Comparing expectation on future interest rates implicit in IRS contracts with realizations of Euribor, we argue whether the financial market provides a safe strategy to investors choosing fixed long-term interest rates against floating ones. The development of European financial market has reached a point that allows some preliminary empirical analysis. Time series are long enough to draw some conclusion, although some exogenous shocks that has afflicted the last decades suggest that more data are needed for a deeper quantitative analysis. Yet, the paper provides support to traders hedging their positions on fixed-income markets

Research paper thumbnail of Insights on the Theory of Robust Games

Economics and Quantitative Methods, 2019

Research paper thumbnail of Set-optimization meets variational inequalities

We study necessary and sufficient conditions to attain solutions of set-optimization problems in ... more We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a solution we deal with has been introduced Heyde and Loehne, for convex set-valued objective functions. To define the set-valued variational inequality, we introduce a set-valued directional derivative and we relate it to the Dini derivatives of a family of linearly scalarized problems. The optimality conditions are given by Stampacchia and Minty type Variational inequalities, defined both by the set valued directional derivative and by the Dini derivatives of the scalarizations. The main results allow to obtain known variational characterizations for vector valued optimization problems.

Research paper thumbnail of Liuc Papers Scrying Europe interbank rates Serie Financial markets and corporate governante 9 Serie: Financial Markets and Corporate Governance SCRYING EUROPE INTERBANK RATES

Research paper thumbnail of Is it safe to play it safe in European interest rates market

Research paper thumbnail of Scrying Europe interbank rates

In this article we test empirical data on European IRS market to check the ability to shape the f... more In this article we test empirical data on European IRS market to check the ability to shape the future and arguing whether the financial market pro vides a safe strategy to investors choosing fixed long-term interest rates against floating one s. Time series are long enough to draw some conclusion, although some exogenous shocks that has afflicted the last decades suggest that more data are needed for a deeper quantitative anal ysis. Yet, the paper provide support to traders hedging their positions on fixed-income mar kets. Nota biografica sugli autori Antonio Caggia Antonio Caggia (Ph.D. Università Cattaneo LIUC, B .Sc. Unievrsità Bocconi) è professore e ricercatore di economia degli intermediari finanzia ri (SSD SECS-P/11) presso l’Università Cattaneo LIUC. I suoi principali temi di ricerca riguardano gli intermediari finanziari, gli strumenti finanziari e derivati, i fondi comuni di investimento, la regolamentazione dei mercati finanziari e la governance delle società quotate. Gi...

Research paper thumbnail of Insights on the Theory of Robust Games

A robust game is a distribution-free model to handle ambiguity generated by a bounded set of poss... more A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization equilibrium, is guaranteed by standard regularity conditions. The paper investigates the sensitivity to the level of uncertainty of this equilibrium. Specifically, we prove that it is an epsilon-Nash equilibrium of the nominal counterpart game, where the epsilon-approximation measures the extra profit that a player would obtain by reducing his level of uncertainty. Moreover, given an epsilon-Nash equilibrium of a nominal game, we prove that it is always possible to introduce uncertainty such that the epsilon-Nash equilibrium is a robust-optimization equilibrium. An example shows that a robust Cournot duopoly model can admit multiple and asymmetric robust-optimization equilibria despite only a symmetric Nash equilibrium exists for the nominal c...

Research paper thumbnail of Anatocismo e ambiguità nei piani di ammortamento

Research paper thumbnail of Set Relations and Approximate Solutions in Set Optimization

arXiv: Optimization and Control, 2018

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and t... more Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a complete lattice-valued one, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared to existing ones in vector and set optimization, and its relevance is shown by means of many examples from vector optimization, statistics and mathematical economics & finance.

Research paper thumbnail of Monotone trajectories of dynamical systems and Clarke's generalized Jacobian

Journal of Inequalities in Pure & Applied Mathematics, 2005

We generalize some results due to Pappalardo and Passacantando [10]. We prove necessary and suffi... more We generalize some results due to Pappalardo and Passacantando [10]. We prove necessary and sufficient conditions for the monotonicity of a trajectory of an autonomous dynamical system with locally Lipschitz data, by means of Clarke’s generalized Jacobian. Some of the results are developed in the framework of variational inequalities.

Research paper thumbnail of Second order optimality conditions for differentiable multiobjective problems

RAIRO - Operations Research, 2000

In this paper some second order necessary and sufficient conditions are given for unconstrained a... more In this paper some second order necessary and sufficient conditions are given for unconstrained and constrained optimization problems involving C 1 functions. A generalized derivative is obtained by approximation with smooth functions and it collapses to Clarke's definition when C 1,1 data are assumed. Furthermore a generalized Taylor's formula is used to prove the conditions.

Research paper thumbnail of First-order optimality conditions in set-valued optimization

Mathematical Methods of Operations Research, 2006

Research paper thumbnail of Some remarks on the Minty vector variational principle

Journal of Mathematical Analysis and Applications, 2008

Research paper thumbnail of Two approaches toward constrained vector optimization and identity of the solutions

Journal of Industrial and Management Optimization, 2005

The recent management literature on multinational corporations (MNCs) has mainly focused on the n... more The recent management literature on multinational corporations (MNCs) has mainly focused on the new role played by subsidiaries within the international firms. Many scholars have underlined that MNCs tend to organise themselves along a differentiated network approach, where subsidiaries play a very different role according to their internal resources and the significance of the local environment. This strategic and organisational model dates back to the pioneering work of Bartlett and Goshal, who called this new international strategy "Transnational" so as to differentiate it from the classical Multidomestic and Global strategies. Along with the different roles played by the subsidiaries, this model is characterised by the simultaneous existence of cooperation and competition within the multinational corporations. The present work focuses on the role of the Italian subsidiary of Agilent Technologies, a multinational firm with around 36,000 employees that is active in more than 40 countries in high-tech sectors such as electronics, telecommunications and life science. The case study brought new light to the usual distinction that is commonly made with regard to the role of a subsidiary. When we try to apply the Transnational model to Agilent we realise that neither this model nor the traditional typologies (Multidomestic, Global) apply to the case we have studied. The role of the subsidiary changes significantly according to the function being considered. Therefore, we conclude that the role of function should be re-evaluated when the strategy and the structure of an MNC is defined. Not only does the classification of subsidiaries change according to the function in question, but the strategic posture and the organisational structure of MNCs should also be re-evaluated in light of the function under consideration. Our study shows how activities such as R&D, where coopetition represents a strategic source of advantage, seem to follow the Transnational scheme, while others such as sales are mainly globally managed.

Research paper thumbnail of Existence of Solutions and Star-shapedness in Minty Variational Inequalities

Journal of Global Optimization, 2005

All rights reserved. No part of this paper may be reproduced in any form without permission of th... more All rights reserved. No part of this paper may be reproduced in any form without permission of the Author. In questi quaderni vengono pubblicati i lavori dei docenti della Facoltà di Economia dell'Università dell'Insubria. La pubblicazione di contributi di altri studiosi, che abbiano un rapporto didattico o scientifico stabile con la Facoltà, può essere proposta da un professore della Facoltà, dopo che il contributo sia stato discusso pubblicamente. Il nome del proponente è riportato in nota all'articolo. I punti di vista espressi nei quaderni della Facoltà di Economia riflettono unicamente le opinioni degli autori, e non rispecchiano necessariamente quelli della Facoltà di Economia dell'Università dell'Insubria. These Working papers collect the work of the Faculty of Economics of the University of Insubria. The publication of work by other Authors can be proposed by a member of the Faculty, provided that the paper has been presented in public. The name of the proposer is reported in a footnote. The views expressed in the Working papers reflect the opinions of the Authors only, and not necessarily the ones of the Economics Faculty of the University of Insubria.

Research paper thumbnail of A Note on a Proof of F. Hahn Concerning the Gross

The aim of this note is to investigate the assumptions and the proofs of some results by F. Hahn,... more The aim of this note is to investigate the assumptions and the proofs of some results by F. Hahn, which have been stated in several other classics of Economic Theory. The results deal with the relations between the gross substitutability and the weak axiom of revealed preference, in a pure exchange economy, ruled by the Walras law.

Research paper thumbnail of Applying Set Optimization to Weak Efficiency

Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the c... more Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend those known for the scalar case. However, in order to introduce a proper definition of variational inequality, some assumptions are usually made that may eventually be questioned. We find two major drawbacks in the papers we considered, that arise when defining generalized derivatives for vector-valued functions. First, some authors introduce set-valued derivatives for single-valued problems, thus completely changing the setting of the problem. Second, when dealing with Dini-type derivatives, infinite elements may occurs. The approach to handle this problem is not yet uniquely defined in the literature, therefore, when considered, the definition proposed may seem arbitrary. Indeed these problems are strictly related with the lack of a complete orde...

Research paper thumbnail of Minty Variational Inequalities and Monotone Trajectories of Differential Inclusions

Journal of Inequalities in Pure & Applied Mathematics, 2004

In (8) the notion of "projected differential equation" has been introduced and the stab... more In (8) the notion of "projected differential equation" has been introduced and the stability of solutions has been studied by means of Stampacchia type variational inequalities. More recently, in (20), Minty variational inequalities have been involved in the study of proper- ties of the trajectories of such a projected differential equation. We consider classical generalizations of both problems, namely projected differential inclusions and variational inequalities with point to set operators, and we extend results stated in (20) to this setting. Moreover, we also apply the results to describe the convergence of the trajectories of a generalized gradient inclusion method.

Research paper thumbnail of Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization

Mathematics of Operations Research

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and t... more Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponding complete lattice of sets. Functions mapping into the preordered set are extended to complete lattice-valued ones, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared with existing ones in vector and set optimization. Its relevance is shown by means of many examples from multicriteria decision making, statistics, and mathematical economics and finance.

Research paper thumbnail of Pointwise and global well-posedness in set optimization: a direct approach

Annals of Operations Research, 2017

The aim of this paper is to characterize some of the pointwise and global wellposedness notions a... more The aim of this paper is to characterize some of the pointwise and global wellposedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.

Research paper thumbnail of Is it safe to play it safe

The future has yet to come but you have a right to shape it. We test empirical data on European I... more The future has yet to come but you have a right to shape it. We test empirical data on European IRS market to check the truthfulness of this sentence. Comparing expectation on future interest rates implicit in IRS contracts with realizations of Euribor, we argue whether the financial market provides a safe strategy to investors choosing fixed long-term interest rates against floating ones. The development of European financial market has reached a point that allows some preliminary empirical analysis. Time series are long enough to draw some conclusion, although some exogenous shocks that has afflicted the last decades suggest that more data are needed for a deeper quantitative analysis. Yet, the paper provides support to traders hedging their positions on fixed-income markets

Research paper thumbnail of Insights on the Theory of Robust Games

Economics and Quantitative Methods, 2019

Research paper thumbnail of Set-optimization meets variational inequalities

We study necessary and sufficient conditions to attain solutions of set-optimization problems in ... more We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a solution we deal with has been introduced Heyde and Loehne, for convex set-valued objective functions. To define the set-valued variational inequality, we introduce a set-valued directional derivative and we relate it to the Dini derivatives of a family of linearly scalarized problems. The optimality conditions are given by Stampacchia and Minty type Variational inequalities, defined both by the set valued directional derivative and by the Dini derivatives of the scalarizations. The main results allow to obtain known variational characterizations for vector valued optimization problems.

Research paper thumbnail of Liuc Papers Scrying Europe interbank rates Serie Financial markets and corporate governante 9 Serie: Financial Markets and Corporate Governance SCRYING EUROPE INTERBANK RATES

Research paper thumbnail of Is it safe to play it safe in European interest rates market

Research paper thumbnail of Scrying Europe interbank rates

In this article we test empirical data on European IRS market to check the ability to shape the f... more In this article we test empirical data on European IRS market to check the ability to shape the future and arguing whether the financial market pro vides a safe strategy to investors choosing fixed long-term interest rates against floating one s. Time series are long enough to draw some conclusion, although some exogenous shocks that has afflicted the last decades suggest that more data are needed for a deeper quantitative anal ysis. Yet, the paper provide support to traders hedging their positions on fixed-income mar kets. Nota biografica sugli autori Antonio Caggia Antonio Caggia (Ph.D. Università Cattaneo LIUC, B .Sc. Unievrsità Bocconi) è professore e ricercatore di economia degli intermediari finanzia ri (SSD SECS-P/11) presso l’Università Cattaneo LIUC. I suoi principali temi di ricerca riguardano gli intermediari finanziari, gli strumenti finanziari e derivati, i fondi comuni di investimento, la regolamentazione dei mercati finanziari e la governance delle società quotate. Gi...

Research paper thumbnail of Insights on the Theory of Robust Games

A robust game is a distribution-free model to handle ambiguity generated by a bounded set of poss... more A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization equilibrium, is guaranteed by standard regularity conditions. The paper investigates the sensitivity to the level of uncertainty of this equilibrium. Specifically, we prove that it is an epsilon-Nash equilibrium of the nominal counterpart game, where the epsilon-approximation measures the extra profit that a player would obtain by reducing his level of uncertainty. Moreover, given an epsilon-Nash equilibrium of a nominal game, we prove that it is always possible to introduce uncertainty such that the epsilon-Nash equilibrium is a robust-optimization equilibrium. An example shows that a robust Cournot duopoly model can admit multiple and asymmetric robust-optimization equilibria despite only a symmetric Nash equilibrium exists for the nominal c...

Research paper thumbnail of Anatocismo e ambiguità nei piani di ammortamento

Research paper thumbnail of Set Relations and Approximate Solutions in Set Optimization

arXiv: Optimization and Control, 2018

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and t... more Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a complete lattice-valued one, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared to existing ones in vector and set optimization, and its relevance is shown by means of many examples from vector optimization, statistics and mathematical economics & finance.

Research paper thumbnail of Monotone trajectories of dynamical systems and Clarke's generalized Jacobian

Journal of Inequalities in Pure & Applied Mathematics, 2005

We generalize some results due to Pappalardo and Passacantando [10]. We prove necessary and suffi... more We generalize some results due to Pappalardo and Passacantando [10]. We prove necessary and sufficient conditions for the monotonicity of a trajectory of an autonomous dynamical system with locally Lipschitz data, by means of Clarke’s generalized Jacobian. Some of the results are developed in the framework of variational inequalities.

Research paper thumbnail of Second order optimality conditions for differentiable multiobjective problems

RAIRO - Operations Research, 2000

In this paper some second order necessary and sufficient conditions are given for unconstrained a... more In this paper some second order necessary and sufficient conditions are given for unconstrained and constrained optimization problems involving C 1 functions. A generalized derivative is obtained by approximation with smooth functions and it collapses to Clarke's definition when C 1,1 data are assumed. Furthermore a generalized Taylor's formula is used to prove the conditions.

Research paper thumbnail of First-order optimality conditions in set-valued optimization

Mathematical Methods of Operations Research, 2006

Research paper thumbnail of Some remarks on the Minty vector variational principle

Journal of Mathematical Analysis and Applications, 2008

Research paper thumbnail of Two approaches toward constrained vector optimization and identity of the solutions

Journal of Industrial and Management Optimization, 2005

The recent management literature on multinational corporations (MNCs) has mainly focused on the n... more The recent management literature on multinational corporations (MNCs) has mainly focused on the new role played by subsidiaries within the international firms. Many scholars have underlined that MNCs tend to organise themselves along a differentiated network approach, where subsidiaries play a very different role according to their internal resources and the significance of the local environment. This strategic and organisational model dates back to the pioneering work of Bartlett and Goshal, who called this new international strategy "Transnational" so as to differentiate it from the classical Multidomestic and Global strategies. Along with the different roles played by the subsidiaries, this model is characterised by the simultaneous existence of cooperation and competition within the multinational corporations. The present work focuses on the role of the Italian subsidiary of Agilent Technologies, a multinational firm with around 36,000 employees that is active in more than 40 countries in high-tech sectors such as electronics, telecommunications and life science. The case study brought new light to the usual distinction that is commonly made with regard to the role of a subsidiary. When we try to apply the Transnational model to Agilent we realise that neither this model nor the traditional typologies (Multidomestic, Global) apply to the case we have studied. The role of the subsidiary changes significantly according to the function being considered. Therefore, we conclude that the role of function should be re-evaluated when the strategy and the structure of an MNC is defined. Not only does the classification of subsidiaries change according to the function in question, but the strategic posture and the organisational structure of MNCs should also be re-evaluated in light of the function under consideration. Our study shows how activities such as R&D, where coopetition represents a strategic source of advantage, seem to follow the Transnational scheme, while others such as sales are mainly globally managed.

Research paper thumbnail of Existence of Solutions and Star-shapedness in Minty Variational Inequalities

Journal of Global Optimization, 2005

All rights reserved. No part of this paper may be reproduced in any form without permission of th... more All rights reserved. No part of this paper may be reproduced in any form without permission of the Author. In questi quaderni vengono pubblicati i lavori dei docenti della Facoltà di Economia dell'Università dell'Insubria. La pubblicazione di contributi di altri studiosi, che abbiano un rapporto didattico o scientifico stabile con la Facoltà, può essere proposta da un professore della Facoltà, dopo che il contributo sia stato discusso pubblicamente. Il nome del proponente è riportato in nota all'articolo. I punti di vista espressi nei quaderni della Facoltà di Economia riflettono unicamente le opinioni degli autori, e non rispecchiano necessariamente quelli della Facoltà di Economia dell'Università dell'Insubria. These Working papers collect the work of the Faculty of Economics of the University of Insubria. The publication of work by other Authors can be proposed by a member of the Faculty, provided that the paper has been presented in public. The name of the proposer is reported in a footnote. The views expressed in the Working papers reflect the opinions of the Authors only, and not necessarily the ones of the Economics Faculty of the University of Insubria.

Research paper thumbnail of A Note on a Proof of F. Hahn Concerning the Gross

The aim of this note is to investigate the assumptions and the proofs of some results by F. Hahn,... more The aim of this note is to investigate the assumptions and the proofs of some results by F. Hahn, which have been stated in several other classics of Economic Theory. The results deal with the relations between the gross substitutability and the weak axiom of revealed preference, in a pure exchange economy, ruled by the Walras law.

Research paper thumbnail of Applying Set Optimization to Weak Efficiency

Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the c... more Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend those known for the scalar case. However, in order to introduce a proper definition of variational inequality, some assumptions are usually made that may eventually be questioned. We find two major drawbacks in the papers we considered, that arise when defining generalized derivatives for vector-valued functions. First, some authors introduce set-valued derivatives for single-valued problems, thus completely changing the setting of the problem. Second, when dealing with Dini-type derivatives, infinite elements may occurs. The approach to handle this problem is not yet uniquely defined in the literature, therefore, when considered, the definition proposed may seem arbitrary. Indeed these problems are strictly related with the lack of a complete orde...

Research paper thumbnail of Minty Variational Inequalities and Monotone Trajectories of Differential Inclusions

Journal of Inequalities in Pure & Applied Mathematics, 2004

In (8) the notion of "projected differential equation" has been introduced and the stab... more In (8) the notion of "projected differential equation" has been introduced and the stability of solutions has been studied by means of Stampacchia type variational inequalities. More recently, in (20), Minty variational inequalities have been involved in the study of proper- ties of the trajectories of such a projected differential equation. We consider classical generalizations of both problems, namely projected differential inclusions and variational inequalities with point to set operators, and we extend results stated in (20) to this setting. Moreover, we also apply the results to describe the convergence of the trajectories of a generalized gradient inclusion method.

Research paper thumbnail of Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization

Mathematics of Operations Research

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and t... more Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponding complete lattice of sets. Functions mapping into the preordered set are extended to complete lattice-valued ones, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared with existing ones in vector and set optimization. Its relevance is shown by means of many examples from multicriteria decision making, statistics, and mathematical economics and finance.