Analysis Seminar

The Department of Mathematics at Western Michigan University will present an analysis seminar on Thursdays.

Day and time: Thursdays, 11 to 11:50 a.m.
Place: 6625 Everett Tower

sept. 20

Optimum Leverage Level of the Banking Sector presented by Sagara Dewasurendra, Department of Mathematics, Western Michigan University

Abstract: Banks make profits from the difference of short-term and long-term loan interests. To issue loans, banks raise funding from capital market. Since the long-term loan rate is relatively stable but short-term interest usually varies, there is an interest risk. Therefore, banks need information about the optimal leverage strategies based on the current economic situation. The recent studies of economic crisis by many economists showed that it was due to "too much" of leveraging by "big banks".

That leveraging turns out to be close to the Kelly's Optimal point. Since Kelly's strategy does not address the risk adequately, in addition we use Return-Drawdown ratio and Inflection point of Kelly's cumulative return curve in finite investment horizon. We consider the random variable of aggregated return and analyze those three optimal points with the best fitted distribution of return with real data. We carry out a sensitivity analysis to determine strategies during a period of interest rates increase, which is the most important and risky period to leverage. Thereafter we consider four types of loans together and examine the derivatives of three points w.r.t the allocation sizes of each loan types to determine how much and how quickly to change leverage or allocation sizes when interest rates increase. These analyses provide bank managers flexible tools to mitigate risk.

sept. 13

Multi-directional Mean Value Inequalities and Dynamic Optimization presented by Yuri Ledyaev, Ph.D., Department of Mathematics, Western Michigan University

Abstract: We discuss recent results on generalized multi-directional mean value inequalities for lower semicontinuous functions for smooth Banach spaces.

Previously, such inequalities have been used to establish relations between Dini derivatives and subgradients of lower semicontinuous functions, to derive metric regularity of functional relations or equivalence of viscosity and minimax solutions in theory of generalized solutions of first-order PDE.

In this talk we demonstrate how the new variant of mean-value inequality can be used to provide derivation of optimality conditions for nonsmooth calculus of variation problems. This is a joint work with Robert Kipka, Ph.D.

sept. 6

Organizational Meeting presented by Jay Treiman, Ph.D., Department of Mathematics, Western Michigan University

Abstract: This is an organizational meeting for those interested in attending and/or giving talks this semester.