Asymptotic Synthesis of Contingent Claims in a Sequence of Discrete-Time Markets

2019 ◽  
Author(s):  
David M. Kreps ◽  
W. Schachermayer
Keyword(s):  
Discrete Time ◽  
Contingent Claims

scholarly journals On the Rate of Convergence of Discrete-Time Contingent Claims

2000 ◽  
Vol 10 (1) ◽  
pp. 53-75 ◽  
Author(s):  
Steve Heston ◽  
Guofu Zhou
Keyword(s):  
Rate Of Convergence ◽  
Discrete Time ◽  
Contingent Claims

Discrete-Time, Minimum-Variance Hedging of European Contingent Claims

2009 ◽  
Author(s):  
Sanjay P. Bhat ◽  
Vijaysekhar Chellaboina ◽  
Anil Bhatia
Keyword(s):  
Discrete Time ◽  
Minimum Variance ◽  
Contingent Claims

No-Arbitrage Valuation of Contingent Claims in Discrete Time

2005 ◽  
Author(s):  
Peter Christoffersen ◽  
Redouane Elkamhi ◽  
Kris Jacobs
Keyword(s):  
Discrete Time ◽  
Contingent Claims ◽  
No Arbitrage

scholarly journals Asymptotic synthesis of contingent claims with controlled risk in a sequence of discrete‐time markets

2021 ◽  
Vol 16 (1) ◽  
pp. 25-47
Author(s):  
David M. Kreps ◽  
Walter Schachermayer
Keyword(s):  
Financial Markets ◽  
Discrete Time ◽  
Continuous Time ◽  
Contingent Claims ◽  
Contingent Claim ◽  
Complete Markets ◽  
Continuous Time Model ◽  
Time Model ◽  
Black Scholes ◽  
Discrete Time Models

We examine the connection between discrete‐time models of financial markets and the celebrated Black–Scholes–Merton (BSM) continuous‐time model in which “markets are complete.” Suppose that (a) the probability law of a sequence of discrete‐time models converges to the law of the BSM model and (b) the largest possible one‐period step in the discrete‐time models converges to zero. We prove that, under these assumptions, every bounded and continuous contingent claim can be asymptotically synthesized, controlling for the risks taken in a manner that implies, for instance, that an expected‐utility‐maximizing consumer can asymptotically obtain as much utility in the (possibly incomplete) discrete‐time economies as she can at the continuous‐time limit. Hence, in economically significant ways, many discrete‐time models with frequent trading resemble the complete‐markets model of BSM.

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