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Probability and Computational Finance Seminar
Tomoyuki Ichiba University of California, Santa Barbara Title: Diffusions with Rank-Based Characteristics and Values in the Nonnegative Quadrant Abstract: We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not both. The construction involves solving a system of coupled Skorokhod reflection equations, then “unfolding” the Skorokhod reflection of a suitable semimartingale in the manner of Prokaj (2009). Questions of pathwise uniqueness and strength are also addressed, for systems of stochastic differential equations with reflection that realize these diffusions. When the variance of the laggard is at least as large as that of the leader, it is shown that the corner of the quadrant is never visited. We also discuss a financial application and recent related work of other authors. This is a joint work with Ioannis Karatzas and Vilmos Prokaj. Date: Monday, November 5, 2012 Time: 5:00 pm Location: Wean Hall 6423 Submitted by: Kasper Larsen |