*****  Note Special Date *****



       Department of Systems Engineering and Engineering Management,

                    The Chinese University of Hong Kong


Risk minimizing portfolios and HJB equations
for stochastic differential games

Professor Bernt Øksendal
University of Oslo

Date : June 15, 2006 (Thursday)

Time : 4:30 p.m. - 5:30 p.m.

Venue : Room 513, William M.W. Mong Engineering Building

(Engineering Building Complex Phase 2), CUHK

In this paper we consider the problem to find a market portfolio that
minimizes the convex risk measure of the terminal wealth in a jump diffusion
market. We formulate the problem as a two player (zero-sum) stochastic
differential game. To help us find a solution, we prove a theorem giving the
HJB conditions for a general zero-sum stochastic differential game in a jump
diffusion setting. We then use the theorem to study particular risk
minimization problems. Finally, we extend our approach to cover general
stochastic differential games (not necessarily zero-sum), and we obtain
similar HJB equations for the Nash equilibriums of such games.

The talk is based on joint work with Sure Mataramvura.

Bernt Øksendal was born 10 April 1945 in Fredrikstad, Norway. Since 1968 he
has been married to Eva Øksendal. They have 3 children. Bernt Øksendal has a
Masters degree in mathematics from the University of Oslo, Norway (1970) and a
Ph.D. degree in mathematics from the University of California, Los Angeles
(UCLA) in 1971. He has been a full professor at the University of Oslo from
1991 and an adjunct professor at the Norwegian School of Economics and
Business Administration (NHH) from 1992.

From 1992 to 1996 he was a VISTA professor, specially appointed by VISTA (a
research cooperation between the Norwegian Academy of Science and Letters and
Statoil) to do research on the applications of stochastic partial differential
equations to enhanced oil recovery in the North Sea.

In 1996 Bernt Øksendal was awarded the Nansen Prize for his research in
stochastic analysis and applications. The same year he was elected member of
the Norwegian Academy of Science and Letters.

Since 1996 he has been the Norwegian coordinator of the "Mathematical
Modeling" program, which is a teaching and research mathematics cooperation
between the University of Oslo and the universities of Southern Africa. This
program has since its start in 1996 produced more than 60 Masters candidates
and about 10 Ph.D.s in mathematics in the Southern African region.

Bernt Øksendal has been a visiting researcher/professor at the following
places: The University of Edinburgh (1971-72 and 1982), UCLA/Caltech (1977-78
and 1984-85), University of California, San Diego (1989) and University of
California, Irvine (1999).

In April 2005 he was elected Chair of the newly established European Science
Foundation program "Advanced Mathematical Methods in Finance" (AMaMeF), which
is a research cooperation between 16 European countries.

Bernt Øksendal has more than 150 publications and he has written/coauthored 4
monographs, including the book "Stochastic Differential Equations", published
by Springer. The 3rd printing of the 6th edition of this book came out in


Note : Cookies and drinks will be available at 4:15 pm.



                       ***** ALL ARE WELCOME *****

Host : Prof. Xunyu Zhou
Tel : 2609 8238
Email : xyzhou@se.cuhk.edu.hk

For more information please

refer to http://www.se.cuhk.edu.hk/~seg5810/