A Nonstandard Approach to Option Pricing

DOI10.1111/j.1467-9965.1991.tb00017.xzbMath0900.90104OpenAlexW2057647905MaRDI QIDQ4345916

P. Ekkehard Kopp, Walter Willinger, Nigel J. Cutland

Publication date: 31 August 1997

Published in: Mathematical Finance (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9965.1991.tb00017.x

zbMATH Keywords

option pricingnonstandard analysisgeometric Brownian motionstochastic analysisnonstandard probability theoryhyperfinite geometric random walk

Mathematics Subject Classification ID

Financial applications of other theories (91G80) Portfolio theory (91G10)

Related Items (10)

Reasoning about negligibility and proximity in the set of all hyperreals ⋮ From binomial expectations to the Black-Scholes formula: The main ideas ⋮ MARGIN TRADING THROUGH HYPER TIMELINE ⋮ Toward A Convergence Theory For Continuous Stochastic Securities Market Models¹ ⋮ A Nonstandard Approach to Option Pricing ⋮ First steps towards an equilibrium theory for Lévy financial markets ⋮ AN INFINITESIMAL ANALYSIS OF THE STOP-LOSS-START-GAIN STRATEGY ⋮ Equilibrium Pricing of Derivative Securities in Dynamically Incomplete Markets ⋮ Binomial valuation of lookback options ⋮ Elementary stochastic calculus for finance with infinitesimals

Cites Work

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• The Pricing of Options and Corporate Liabilities
• Foundations of infinitesimal stochastic analysis
• Pathwise stochastic integration and applications to the theory of continuous trading
• Martingales and arbitrage in multiperiod securities markets
• Martingales and stochastic integrals in the theory of continuous trading
• Oligopoly in markets with a continuum of traders: An asymptotic interpretation
• Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations.I
• Martingales and Stochastic Integrals
• Strong Core Theorems with Nonconvex Preferences
• Optimal Stopping of Two-Parameter Processes on Nonstandard Probability Spaces
• Core Theory with Strongly Convex Preferences
• Star-Finite Representations of Measure Spaces
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• Nonstandard Exchange Economies
• An Elementary Core Equivalence Theorem
• A Nonstandard Approach to Option Pricing
• From Discrete‐ to Continuous‐Time Finance: Weak Convergence of the Financial Gain Process¹
• The analysis of finite security markets using martingales
• Option pricing: A simplified approach
• Markets with a Continuum of Traders

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