Asset price bubbles, wealth preserving, dominating, and replicating trading strategies

Robert Jarrow; Yuxuan Liu

doi:10.3934/fmf.2023002

Article Contents

2023, Volume 2, Issue 1: 33-55. Doi: 10.3934/fmf.2023002 open access

This issue Previous Article Total positivity and relative convexity of option prices Next Article Power laws in market microstructure

Asset price bubbles, wealth preserving, dominating, and replicating trading strategies

Robert Jarrow^1, , and
Yuxuan Liu^2,

1.
Samuel Curtis Johnson Graduate School of Management, Cornell University, Ithaca, N. Y. 14853
2.
Operations Research and Industrial Engineering, Cornell University, Ithaca, N. Y. 14853

^*Corresponding author: Robert Jarrow
^*Corresponding author: Robert Jarrow

Received: June 2022

Revised: August 2022

Early access: February 2023

Published: March 2023

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Abstract

This paper studies an arbitrage-free, competitive and frictionless market with trading in a single risky asset and money market account, where the risky asset exhibits a price bubble. We analyze two sets of self-financing and admissible trading strategies in this market. The first are simple trading strategies, and the second are trading strategies that replicate or super-replicate the risky asset's payoffs at the model's horizon. We show that in both sets there exist wealth preserving trading strategies, i.e. trading strategies whose initial value equals the present value of its future cash flows. And, in the second set, we show that there are wealth preserving replicating trading strategies that dominate buying and holding the risky asset. The practical applications of these insights are discussed.

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Mathematics Subject Classification: Primary: 91G30, 58F17; Secondary: 53C35.

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