scholarly journals A new definition of the integral for non-parametric problems in the calculus of variations

1959 ◽  
Vol 102 (1-2) ◽  
pp. 23-32 ◽  
Author(s):  
James Serrin
Keyword(s):  
Calculus Of Variations ◽  
Parametric Problems ◽  
Definition Of ◽  
Non Parametric

Which One is More Important Factor for Pricing Options, Skewness or Kurtosis?

2006 ◽  
Vol 14 (2) ◽  
pp. 25-50
Author(s):  
Sol Kim
Keyword(s):  
Parametric Method ◽  
Estimation Method ◽  
Relative Importance ◽  
Pricing Options ◽  
Pricing Errors ◽  
Risk Neutral ◽  
Definition Of ◽  
Skewness And Kurtosis ◽  
Non Parametric

This paper investigates the relative importance of the skewness and kurtosis of the risk neutral distribution for pricing KOSPI200 options. The skewness and kurtosis are estimated from non parametric method of Bakshi, Kapadia, and Madan (2003) and the parametric method of Corrado and Su (1996). We show that the skewness of the risk neutral distribution is more important factor than the kurtosis irrespective of the estimation method, the definition of pricing errors, the moneyness, the type of options and a period of time.

Optimality Principles for Fuzzy Dual Uncertain Systems

2018 ◽  
pp. 47-72
Author(s):  
Félix Mora-Camino ◽  
Hakim Bouadi ◽  
Roger Marcelin Faye ◽  
Lunlong Zhong
Keyword(s):  
Optimality Conditions ◽  
Calculus Of Variations ◽  
Optimization Problems ◽  
Lagrange Equation ◽  
Necessary Optimality Conditions ◽  
Continuous System ◽  
Propagation Of Uncertainty ◽  
Performance Indexes ◽  
Definition Of ◽  
Optimality Principles

This chapter considers the extension of the calculus of variations to the optimization of a class of fuzzy systems where the uncertainty of variables and parameters is represented by symmetrical triangular membership functions. The concept of fuzzy dual numbers is introduced, and the consideration of the necessary differentiability conditions for functions of dual variables leads to the definition of fuzzy dual functions. It is shown that when this formalism is adopted to represent performance indexes for uncertain optimization problems, the calculus of variations can be used to establish necessary optimality conditions as an extension to this case of the Euler-Lagrange equation. Then the chapter discusses the propagation of uncertainty when the fuzzy dual formalism is adopted for the state representation of a time continuous system. This leads to the formulation of a fuzzy dual optimization problem for which necessary optimality conditions, corresponding to an extension of Pontryagine's optimality principle, are established.

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