The Hebrew University of Jerusalem
**
The Edmund Landau Minerva Center for Research in Mathematical
Analysis and Related Areas**

#
THE LANDAU LECTURES 2004/2005

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Professor HANS FÖLLMER
(Humboldt University, Berlin)

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will deliver three lectures on:

PROBABILISTIC ASPECTS OF FINANCIAL RISK

- Thursday, March 3
^{rd}, 2005
**Stochastic analysis of financial options**
- The price fluctuation of liquid financial assets is usually modeled as
a stochastic process
which satisfies some form of the "efficient markets hypothesis". Such
assumptions
can be made precise in terms of martingale measures. We discuss the
role of these martingale measures
in analyzing financial derivatives such as options, viewed as
non-linear functionals of the underlying stochastic process. Uniqueness
of the martingale measure
provides the mathematical key to a perfect "hedge" of a financial
derivative by means of a dynamic trading strategy in the underlying
assets, and in particular to pricing formulas of Black-Scholes type.
But for realistic models the martingale measure is no longer unique,
and intrinsic risks appear on the level of derivatives. We discuss
various mathematical approaches to the problem of pricing and hedging
in such a setting.

- Sunday, March 6
^{th}, 2005
**Quantifying the risk: a robust view**
- In recent years, there has been an increasing focus on the problem of
quantifying the risk of a financial position, in particular from the
point of view of a supervising agency. We discuss some mathematical
developments in this area of financial risk management, in particular
representation results for convex risk measures which take model
uncertainty into account, and some robust optimization problems which
arise in this context.

- Tuesday, March 8
^{th}, 2005
**Dynamic risk measures**
- The problems of quantifying the risk of a stochastic payment stream and
of updating a risk assessment in the light of incoming information have
led to a theory of dynamic risk measures. We discuss some recent
developments, in particular the connections to the pricing problem for
American options and to the theory of backward stochastic differential
equations.

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**Last updated**: Feb. 27th, 2005

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