The aim of this work is to present a modification of the standard binomial method which allows to... more The aim of this work is to present a modification of the standard binomial method which allows to price American barrier options improving the efficiency of the trinomial methods. Our approach is based on a suitable interpolation of binomial values and allows to price and hedge such options also in the critical case of near barriers. All the different types
We introduce a new numerical approach, called “Singular points method”, for pricing path-dependen... more We introduce a new numerical approach, called “Singular points method”, for pricing path-dependent options. This method, based on a continuous representation of the price at every node of the binomial tree, allows to obtain very precise upper and lower bounds of the pure discrete binomial price reducing drastically the time of computation. The method allows also to provide a-priori estimates of the difference between an upper and a lower bound. We apply the method to the case of Asian and lookback American options.
The search for optimality is a must in the study of biological evolution and many models have bee... more The search for optimality is a must in the study of biological evolution and many models have been proposed in order to grasp its main operating gears. These models can also give a deep comprehension of many social and economical phenomena and are studied in the so called econophysics. Bak Sneppen is one of the most significant models because it balances at best explication power and simplicity. Unlike cellular automata models, where phenomena happen in a local framework without global supervision, Bak Sneppen models join locality and globality, as many contemporary economical models require. The authors try to re-read these models between utopic and dystopic frames, showing with simplified models some behaviors that had not been considered in the previous literature. A search for uniformity rather than optimality is also studied, since it seems to rule fashion evolution, as well as political behavior of people (Band wagon).
The search of a hierarchy in economic systems, using triangulation method, has a long tradition i... more The search of a hierarchy in economic systems, using triangulation method, has a long tradition in economics. This study, after revisiting Authors' optimization algorithm, based on "path restricted unimodularity", tries to cast new light into the black box of the rules governing the transformation of the economic structure in growth process. The method developed and used by the authors has a very simple code, and, in its enhanced version, even when it does not succeed Inter-temporal, cross-sectional and simulated comparisons have been made on in solving the optimality problem it gives very strict bounds from below and from above for the optimal solution. In the present study the exact solution was reached in 42 cases out of 44, and in the remaining two cases the confidence interval was less than 10 ^4. European Community, Union and Euro Area input-output tables (1965-2007) have been analyzed aiming at verifying above all whether the asymmetrical hierarchy prevailed or ...
ABSTRACT We deal with measures on Δ--semigroups, in particular on MV-algebras. Examples of such m... more ABSTRACT We deal with measures on Δ--semigroups, in particular on MV-algebras. Examples of such measures are T∞-valuations on clans of fuzzy sets. We first provide the Hahn decomposition theorem for measures on Δ--semigroups. This is then used to obtain a representation theorem for such measures, which itself is a basic tool in the proof of Liapounoff type theorems.
Rendiconti del Circolo Matematico di Palermo, 1998
We prove the Nikodym Boundedness, Brooks-Jewett and Vitali-Hahn-Saks theorems for modular functio... more We prove the Nikodym Boundedness, Brooks-Jewett and Vitali-Hahn-Saks theorems for modular functions on orthomodular lattices with SIP and on particular complemented or sectionally complemented lattices, and the equivalence, for any complemented or sectionally complemented lattice, between the Brooks-Jewett and Vitali-Hahn-Saks theorems for group-valued modular functions. As consequence, we obtain characterizations of relative, sequential and weak compactness in spaces of modular
The aim of this work is to present a modification of the standard binomial method which allows to... more The aim of this work is to present a modification of the standard binomial method which allows to price American barrier options improving the efficiency of the trinomial methods. Our approach is based on a suitable interpolation of binomial values and allows to price and hedge such options also in the critical case of near barriers. All the different types
We introduce a new numerical approach, called “Singular points method”, for pricing path-dependen... more We introduce a new numerical approach, called “Singular points method”, for pricing path-dependent options. This method, based on a continuous representation of the price at every node of the binomial tree, allows to obtain very precise upper and lower bounds of the pure discrete binomial price reducing drastically the time of computation. The method allows also to provide a-priori estimates of the difference between an upper and a lower bound. We apply the method to the case of Asian and lookback American options.
The search for optimality is a must in the study of biological evolution and many models have bee... more The search for optimality is a must in the study of biological evolution and many models have been proposed in order to grasp its main operating gears. These models can also give a deep comprehension of many social and economical phenomena and are studied in the so called econophysics. Bak Sneppen is one of the most significant models because it balances at best explication power and simplicity. Unlike cellular automata models, where phenomena happen in a local framework without global supervision, Bak Sneppen models join locality and globality, as many contemporary economical models require. The authors try to re-read these models between utopic and dystopic frames, showing with simplified models some behaviors that had not been considered in the previous literature. A search for uniformity rather than optimality is also studied, since it seems to rule fashion evolution, as well as political behavior of people (Band wagon).
The search of a hierarchy in economic systems, using triangulation method, has a long tradition i... more The search of a hierarchy in economic systems, using triangulation method, has a long tradition in economics. This study, after revisiting Authors' optimization algorithm, based on "path restricted unimodularity", tries to cast new light into the black box of the rules governing the transformation of the economic structure in growth process. The method developed and used by the authors has a very simple code, and, in its enhanced version, even when it does not succeed Inter-temporal, cross-sectional and simulated comparisons have been made on in solving the optimality problem it gives very strict bounds from below and from above for the optimal solution. In the present study the exact solution was reached in 42 cases out of 44, and in the remaining two cases the confidence interval was less than 10 ^4. European Community, Union and Euro Area input-output tables (1965-2007) have been analyzed aiming at verifying above all whether the asymmetrical hierarchy prevailed or ...
ABSTRACT We deal with measures on Δ--semigroups, in particular on MV-algebras. Examples of such m... more ABSTRACT We deal with measures on Δ--semigroups, in particular on MV-algebras. Examples of such measures are T∞-valuations on clans of fuzzy sets. We first provide the Hahn decomposition theorem for measures on Δ--semigroups. This is then used to obtain a representation theorem for such measures, which itself is a basic tool in the proof of Liapounoff type theorems.
Rendiconti del Circolo Matematico di Palermo, 1998
We prove the Nikodym Boundedness, Brooks-Jewett and Vitali-Hahn-Saks theorems for modular functio... more We prove the Nikodym Boundedness, Brooks-Jewett and Vitali-Hahn-Saks theorems for modular functions on orthomodular lattices with SIP and on particular complemented or sectionally complemented lattices, and the equivalence, for any complemented or sectionally complemented lattice, between the Brooks-Jewett and Vitali-Hahn-Saks theorems for group-valued modular functions. As consequence, we obtain characterizations of relative, sequential and weak compactness in spaces of modular
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