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Asset price bubbles in markets with transaction costs

  • *Corresponding author: Thomas Reitsam

    *Corresponding author: Thomas Reitsam

The financial support of the Verein zur Versicherungswissenschaft München e.V. is gratefully acknowledged

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  • We study asset price bubbles in market models with proportional transaction costs $ \lambda\in (0, 1) $ and finite time horizon $ T $ in the setting of [49]. By following [29], we define the fundamental value $ F $ of a risky asset $ S $ as the price of a super-replicating portfolio for a position terminating in one unit of the asset and zero cash. We then obtain a dual representation for the fundamental value by using the super-replication theorem of [50]. We say that an asset price has a bubble if its fundamental value differs from the ask-price $ (1+\lambda)S $. We investigate the impact of transaction costs on asset price bubbles and show that our model intrinsically includes the birth of a bubble.

    Mathematics Subject Classification: Primary: 91G99, 91B70; Secondary: 60G44.


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  • Figure 1.  Example 4: Simulation of $ 253 $ days of $ S $, defined in 60 with $ \mu = 0.3 $, $ \sigma_0 = 0.4 $ and the starting time $ \gamma $ of the bubble being uniformly distributed on $ (0, 1) $. Before $ \gamma $ the fundamental value coincides with $ (1+\lambda)S $. When $ \gamma $ occurs, the fundamental value drops to $ 0 $

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