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Probability and Computational Finance Seminar
Sergio Pulido Department of Information Engineering and Operations Research Cornell University Title: Bubbles and contingent claims in markets with short-sale constraints Abstract: The current financial crisis, product of the burst of the alleged real estate bubble, has increased the interest of the financial and academic community in the causes and implications of asset price bubbles. In recent works Jarrow, Protter and Shimbo (2006, 2008) and Cox and Hobson (2005) developed an arbitrage-free pricing theory for bubbles in complete and incomplete markets. These papers approach the subject by using the insights and tools of mathematical finance, rather than equilibrium arguments where substantial structure, such as investor optimality and market clearing mechanisms, has to be imposed. In their framework, bubbles occur because the market's valuation measure is a local martingale measure which is not a martingale measure and hence the discounted asset's price is above the expectation of its future cash-flows. The existence of bubbles does not contradict the condition of no free lunch with vanishing risk (NFLVR), because short-sale constraints, given by an admissibility condition on the set of trading strategies, do not allow investors to make a riskless profit from the overpriced securities. In an attempt to combat sharp and extreme declines in certain stock prices related to the bursting of these bubbles, both the British and the American government imposed temporary bans on the short selling of certain categories of stocks. This affects the liquidity of stocks, and has other less obvious effects.The aim of this talk is to explain how the previous work extends to models where some assets cannot be sold short whatsoever and explore how financial instruments could behave in such models. Date: Monday, February 22, 2010 Time: 5:00 pm Location: Wean Hall 6423 |