Abstract
Speculative episodes typically involve leverage. For example, the well known tulipmania episode was accompanied by the introduction of foward contracts which allowed speculators to take leveraged positions in tulip bulbs. The Great Crash of 1929 was exacerbated by leveraged trusts which used leverage to buy stocks. These leveraged trusts could in turn be bought on margin which allowed speculators to hold highly leveraged positions. More recently, speculation in the housing market was accompanied by extreme leverage. In this paper, I provide a continuous time extension of the Harrison-Kreps(1978) speculative model with learning. Speculators have heterogeneous priors and learn about the unknown switching intensity between states. When the riskless rate is fixed, the speculative premium for each investor is determined by the expected present value of excess demand in the consumption and bond markets. Letting the riskless rate adjust so that the market for borrowing clears provides endogenous margin requirements which limit borrowing. In addition, the wealth distribution of speculators now becomes a determinant of speculative premia and a fairly rich set of speculative dynamics arise.
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