International Journal of Approximate Reasoning, Sep 1, 2020
Abstract The Average Cumulative representation of fuzzy intervals is connected with the possibili... more Abstract The Average Cumulative representation of fuzzy intervals is connected with the possibility theory in the sense that the possibility and necessity functions are substituted by a pair of non decreasing functions defined as the positive and negative variations in the Jordan decomposition of a membership function. In this paper we motivate the crucial role of ACF in determining the membership function from experimental data; some examples and simulations are shown to state the robustness of the proposed construction.
European Journal of Operational Research, May 1, 2005
Many numerical aspects are involved in parameter estimation of stochastic volatility models. We i... more Many numerical aspects are involved in parameter estimation of stochastic volatility models. We investigate a model for stochastic volatility suggested by Hobson and Rogers [Complete models with stochastic volatility, Mathematical Finance 8 (1998) 27] and we focus on its ...
ABSTRACT Financial problems are often based on a rigorous mathematical struc-ture and are strongl... more ABSTRACT Financial problems are often based on a rigorous mathematical struc-ture and are strongly dependent on the imprecision of the input data. In this paper we show how it is possible to model the uncertainty by assuming that the fundamental parameters are fuzzy numbers. The massive computation effort involved in computations, can be success-fully handled due to a flexible and precise parametric representation of the lower and upper branches of the membership functions of the fuzzy numbers.
European Society for Fuzzy Logic and Technology Conference, 2009
About three decades ago, Dubois and Prade developed the arithmetical structure of fuzzy numbers a... more About three decades ago, Dubois and Prade developed the arithmetical structure of fuzzy numbers and they introduced the well known LR model and the corresponding formulas for the fuzzy operations (see the recent publication [1] and the references therein). The arithmetic calculations ...
In this paper we show that the so called fuzzy--stochastic approach in financial models is an eff... more In this paper we show that the so called fuzzy--stochastic approach in financial models is an efficient way to handle the uncertainty about parameters. We show the possible applications in the option pricing models with a constant and stochastic volatility. Fuzzy numbers, extension principle, sensitivity analysis, fuzzy stochastic approach in financial models, option pricing models
Interval linear programming (ILP) has a long history but it still reserves many interesting sugge... more Interval linear programming (ILP) has a long history but it still reserves many interesting suggestions when it is applied to model real problems that are indivisible by uncertainty. In this paper we apply the comparison index for interval ordering based on the generalized Hukuhara difference to compare solutions in the ILP and we analyse the robustness of our methodology.
2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2017
Linear Programming problems are solved in the present paper when uncertainty in costs is modelled... more Linear Programming problems are solved in the present paper when uncertainty in costs is modelled through interval numbers; the comparison index based on the generalized Hukuhara difference is adopted to indicate the possible relative positions of two intervals and to chose the proper solution.
We present new results in interval analysis (IA) and in the calculus for interval-valued function... more We present new results in interval analysis (IA) and in the calculus for interval-valued functions of a single real variable. Starting with a recently proposed comparison index, we develop a new general setting for partial order in the (semi linear) space of compact real intervals and we apply corresponding concepts for the analysis and calculus of interval-valued functions. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in calculus. Concepts related to convergence and limits, continuity, gH-differentiability and monotonicity of interval-valued functions are introduced and analyzed in detail. Graphical examples and pictures accompany the presentation. A companion Part II of the paper will present additional properties (max and min points, convexity and periodicity).
International Journal of Approximate Reasoning, Sep 1, 2020
Abstract The Average Cumulative representation of fuzzy intervals is connected with the possibili... more Abstract The Average Cumulative representation of fuzzy intervals is connected with the possibility theory in the sense that the possibility and necessity functions are substituted by a pair of non decreasing functions defined as the positive and negative variations in the Jordan decomposition of a membership function. In this paper we motivate the crucial role of ACF in determining the membership function from experimental data; some examples and simulations are shown to state the robustness of the proposed construction.
European Journal of Operational Research, May 1, 2005
Many numerical aspects are involved in parameter estimation of stochastic volatility models. We i... more Many numerical aspects are involved in parameter estimation of stochastic volatility models. We investigate a model for stochastic volatility suggested by Hobson and Rogers [Complete models with stochastic volatility, Mathematical Finance 8 (1998) 27] and we focus on its ...
ABSTRACT Financial problems are often based on a rigorous mathematical struc-ture and are strongl... more ABSTRACT Financial problems are often based on a rigorous mathematical struc-ture and are strongly dependent on the imprecision of the input data. In this paper we show how it is possible to model the uncertainty by assuming that the fundamental parameters are fuzzy numbers. The massive computation effort involved in computations, can be success-fully handled due to a flexible and precise parametric representation of the lower and upper branches of the membership functions of the fuzzy numbers.
European Society for Fuzzy Logic and Technology Conference, 2009
About three decades ago, Dubois and Prade developed the arithmetical structure of fuzzy numbers a... more About three decades ago, Dubois and Prade developed the arithmetical structure of fuzzy numbers and they introduced the well known LR model and the corresponding formulas for the fuzzy operations (see the recent publication [1] and the references therein). The arithmetic calculations ...
In this paper we show that the so called fuzzy--stochastic approach in financial models is an eff... more In this paper we show that the so called fuzzy--stochastic approach in financial models is an efficient way to handle the uncertainty about parameters. We show the possible applications in the option pricing models with a constant and stochastic volatility. Fuzzy numbers, extension principle, sensitivity analysis, fuzzy stochastic approach in financial models, option pricing models
Interval linear programming (ILP) has a long history but it still reserves many interesting sugge... more Interval linear programming (ILP) has a long history but it still reserves many interesting suggestions when it is applied to model real problems that are indivisible by uncertainty. In this paper we apply the comparison index for interval ordering based on the generalized Hukuhara difference to compare solutions in the ILP and we analyse the robustness of our methodology.
2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2017
Linear Programming problems are solved in the present paper when uncertainty in costs is modelled... more Linear Programming problems are solved in the present paper when uncertainty in costs is modelled through interval numbers; the comparison index based on the generalized Hukuhara difference is adopted to indicate the possible relative positions of two intervals and to chose the proper solution.
We present new results in interval analysis (IA) and in the calculus for interval-valued function... more We present new results in interval analysis (IA) and in the calculus for interval-valued functions of a single real variable. Starting with a recently proposed comparison index, we develop a new general setting for partial order in the (semi linear) space of compact real intervals and we apply corresponding concepts for the analysis and calculus of interval-valued functions. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in calculus. Concepts related to convergence and limits, continuity, gH-differentiability and monotonicity of interval-valued functions are introduced and analyzed in detail. Graphical examples and pictures accompany the presentation. A companion Part II of the paper will present additional properties (max and min points, convexity and periodicity).
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