Infinitesimal Analysis and Hypermodels

2003 ◽  
pp. 29-38
Keyword(s):  
Infinitesimal Analysis

AN INFINITESIMAL ANALYSIS OF THE STOP-LOSS-START-GAIN STRATEGY

2005 ◽  
Vol 08 (05) ◽  
pp. 623-633 ◽  
Author(s):  
SIU-AH NG
Keyword(s):  
Trading Strategy ◽  
Elementary Derivation ◽  
Riemann Sum ◽  
Black Scholes ◽  
Infinitesimal Analysis ◽  
Stop Loss

The paradox of the Stop-Loss-Start-Gain trading strategy is resolved by showing that along the hyperfinite timeline the strategy incurs infinitesimal losses summing up to a non-infinitesimal amount. As a consequence, the Black–Scholes formula is derived using only hyperreal arithmetic and Riemann sum, probably the most elementary derivation thus far.

Naive Foundations of Infinitesimal Analysis

2002 ◽  
pp. 10-34
Author(s):  
E. I. Gordon ◽  
A. G. Kusraev ◽  
S. S. Kutateladze
Keyword(s):  
Infinitesimal Analysis

scholarly journals Некоторые замечания о нестандартных методах анализа. I

2019 ◽  
Author(s):  
E.I. Gordon
Keyword(s):  
Predicate Logic ◽  
Continuum Hypothesis ◽  
Original Method ◽  
Formal Proofs ◽  
Forthcoming Article ◽  
First Order ◽  
Boolean Valued Analysis ◽  
History Of ◽  
Infinitesimal Analysis ◽  
The Axiom Of Choice

This and forthcoming articles discuss two of the most known nonstandard methods of analysis---the Robinsons infinitesimal analysis and the Boolean valued analysis, the history of their origination, common features, differences, applications and prospects. This article contains a review of infinitesimal analysis and the original method of forcing. The presentation is intended for a reader who is familiar only with the most basic concepts of mathematical logic---the language of first-order predicate logic and its interpretations. It is also desirable to have some idea of the formal proofs and the Zermelo--Fraenkel axiomatics of the set theory. In presenting the infinitesimal analysis, special attention is paid to formalizing the sentences of ordinary mathematics in a first-order language for a superstructure. The presentation of the forcing method is preceded by a brief review of C.Godels result on the compatibility of the Axiom of Choice and the Continuum Hypothesis with Zermelo--Fraenkels axiomatics. The forthcoming article is devoted to Boolean valued models and to the Boolean valued analysis, with particular attention to the history of its origination.

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