A partial introduction to financial asset pricing theory.
type: Item
instance of: scholarly article
title: A partial introduction to financial asset pricing theory.
zbMATH Open document ID: 1048.91067
DOI: 10.1016/S0304-4149(00)00064-8
published in: Stochastic Processes and their Applications
publication date: 2004-09-22T00:00:00Z
review text: The paper offers an overview of the semimartingale theory results about financial asset pricing in continuous time, based on the well-established arbitrage-free market approach. In the standard review part, the author concentrates on the exact conditions of the arbitrage-free asset pricing in terms of the existence and uniqueness of the equivalent martingale measure for the given semimartingale price process. The traditional application to European option pricing via a self-financing replicating investment strategy is spelled out. In the less ``textbook'' part of the paper, pricing of general lookback (path-dependent) options is put in connection with the Clark-Ocone formula for Brownian functionals. Specifically, prices of American options are characterized by means of the Snell envelope of the option payoff process. A result from specialized literature about an alternative American put option pricing formula, which connects the put price to the solution of a backward stochastic differential equation with an obstacle, is explained.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 2102366
zbMATH Keywords: complete markets
zbMATH Keywords: arbitrage
zbMATH Keywords: backwards stochastic differential equation
author: Philip Protter
reviewed by: Alexis Derviz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2102366