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

### Day and time: Thursdays, 11 a.m.

Place: 6625 Everett Tower

## Upcoming Talks

### Jan. 16

**Organizational Meeting **presented by Yuri Ledyaev, Ph.D., Department of Mathematics, Western Michigan University

Abstract: This is a brief organizational meeting to discuss a program for Analysis Seminar (this is also Math 6970-Seminar in Applied Mathematics) for the Spring 2020 semester. Everyone who is interested in analysis, applied mathematics and their applications (in particular, in optimization, control theory, differential equations, mathematical finance, mathematical biology, etc.) is invited.

## Past Talks

### Oct. 10

**Bank Balance Sheet Risk Allocation **presented by Jim Zhu, Ph.D., Department of Mathematics, Western Michigan University

Abstract: I will present a linear programming (LP) model for a real bank risk management problem. Using linear programming duality we derive a simple and explicit solution. What's interesting is both primal and dual solutions have clear financial interpretations and they provide useful guidance to banking practice.

This is a joint research project with Dr. Pedro Júdice from Societe Generale Bank, Lisbon, Portgual.

### Oct. 3

**Program Maximin for Differential Games with Nonsmooth Data **presented by Yuri Ledyaev, Ph.D., Department of Mathematics, Western Michigan University

Abstract: We consider a differential game with dynamics described by a differential equation

x(t) = f(x(t), u(t), v(t)), x(0) = x_{0}

where x(t) in R^{n} is a state vector, u(t) in U and v(t) in V are controls of players. The first player aims at minimizing the value of the cost functional

l(x(T))

and the second player tries to maximize it. The characteristic feature of the differential game is that players use feedback controls u(t) = k(t, x(t)), v(t) = m(t, x(t)). In this talk we discuss recent results on conditions which imply the representation of the value function as more simpler program maximin function, namely

c(t_{0}, x_{0}) = sup inf l(x(T; t_{0}, x_{0}, u(.), v(.)))

v(.) u(.)

### Sept. 26

**Organizational Meeting **presented by Yuri Ledyaev, Ph.D., Department of Mathematics, Western Michigan University

Abstract: This is a brief organizational meeting to discuss a program for Analysis Seminar (this is also Math 6970-Seminar in Applied Mathematics) for the Fall 2019 semester. Everyone who is interested in analysis, applied mathematics and their application (in particular, in optimization, control theory, differential equations, mathematical finance, mathematical biology, etc.) is invited.