Abstract:
 (1)In this talk, we develop the ratio processes $\{Y_i(t) \}_{t \ge 0}$, i=1,2,\cdots,n, induced from the meanfield BouchaudMezard model. The limit $m_i$ of the longtime average of the ratio process $\{Y_i(t) \}_{t \ge 0}$ is studied and compared with all others. We shows that a strictly increasing sequence $\{\sigma_k \}_{k=1}^{n}$ of the investment volatilities implies a strictly decreasing sequence $\{m_k \}_{k=1}^{n}$ of the limits, given appropriate J, based on both theoretical and numerical analyses. It reveals a negative correlation between the investment volatilities and the ratio processes. As an empirical application, this negative correlation can be employed to characterize the meanfield BouchaudMezard model. Our main result also indicates that an agent whose spontaneous growth or decrease in wealth due to investment in stock markets is always small will eventually become rich in the meanfield BouchaudMezard model.
(2) In this talk we consider the mathematical study of a class of models with large trader and insider characteristics. Indeed, we are interested in the case where the impact of the large trades in the price of one risky asset is a linear function in the policy of the large trader, and the information of the insider is the final price plus a blurring noise that disappears as the final time approaches. Under such a setting our objective is to maximize the logarithmic expected utility function. This is a joint work with Prof. Arturo KohatsuHiga (Osaka University).
