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J. D. Duffie and P. Protter, “From Discrete to Continuous Time Finance: Weak Convergence of the Financial Gain Process,” Stanford University, Stanford, 1988.

has been cited by the following article:

• TITLE: On the Internal Consistency of the Black-Scholes Option Pricing Model

  AUTHORS: Jeremy Berkowitz

  KEYWORDS: Diffusions; Binomial Model; Arbitrage

  JOURNAL NAME: Theoretical Economics Letters, Vol.3 No.3, June 13, 2013

  ABSTRACT: We study the information structure implied by models in which the asset price is always risky and there are no arbitrage opportunities. Using the martingale representation of Harrison and Kreps [1], a claim takes its value from the stream of discounted expected payments. Equivalently, a pricing-kernel is sufficient to value the payment stream. If a price process is always risky, then either the payment or the discount factor must also be continually risky. This observation substantially complicates the valuation of contingent claims. Many classical option pricing formulas abstract from both risky dividends and risky discount rates. In order to value contingent claims, one of the assumptions must be abandoned.