Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/105364
Authors: 
LeRoy, Stephen F.
Year of Publication: 
2012
Citation: 
[Journal:] Contemporary Economics [ISSN:] 2084-0845 [Publisher:] Vizja Press & IT [Place:] Warsaw [Volume:] 6 [Year:] 2012 [Issue:] 4 [Pages:] 54-60
Abstract: 
In continuous-time stochastic calculus a limit in probability is used to extend the definition of the stochastic integral to the case where the integrand is not square-integrable at the endpoint of the time interval under consideration. When the extension is applied to portfolio strategies, absence of arbitrage in finite portfolio strategies is consistent with existence of arbitrage in infinite portfolio strategies. The doubling strategy is the most common example. We argue that this extension may or may not make economic sense, depending on whether or not one thinks that valuation should be continuous. We propose an alternative extension of the definition of the stochastic integral under which valuation is continuous and absence of arbitrage is preserved. The extension involves appending a date and state called to the payoff index set and altering the definition of convergence under which gains on infinite portfolio strategies are defined as limits of gains on finite portfolio strategies.
Subjects: 
infinite time
portfolios
doubling strategy
weak topology
martingale
Ito integral
Radon-Nikodym derivative
JEL: 
J00
Persistent Identifier of the first edition: 
Document Type: 
Article
Appears in Collections:

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.