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 [ 48 ]. By following [ 27 ], 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 [ 49 ]. 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.
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 [ 28 ], 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.
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