Abstracts

The notion of an asset price bubble has two ingredients. One is the observed market price of a given financial asset, the other is the asset's intrinsic value, and the bubble is defined as the difference between the two. The intrinsic value, also called the fundamental value of the asset, is usually defined as the expected sum of future discounted dividends. Here we study a flow in the space of equivalent martingale measures and focus on the corresponding shifting perception of the fundamental value of a given asset in an incomplete financial market model. This allows us to capture the birth of a perceived bubble and to describe it as an initial submartingale which then turns into a supermartingale before it falls back to its initial value zero. We illustrate our results in two examples, one due to Delbaen and Schachermayer [2] and the other given by a a variant of the stochastic volatility model discussed by Sin in [3]. This talk is based on the paper [1].

[1] Biagini F., Föllmer H., Nedelcu S. Shifting Martingale Measures and the Birth of a Bubble as a Submartingale, Finance and Stochastics, accepted, 2013.
[2] F. Delbaen and W. Schachermayer. A simple counter-example to several problems in the theory of asset pricing. Mathematical Finance, 8:1-12, 1998.
[3] C.A. Sin. Complications with stochastic volatility models. Advances in Applied Probability, 30(1):256-268, 1998.