HUJI The Hebrew University of Jerusalem

The Edmund Landau Minerva Center for Research in Mathematical Analysis and Related Areas

THE LANDAU LECTURES 2004/2005

Professor HANS FÖLLMER (Humboldt University, Berlin)

will deliver three lectures on:

PROBABILISTIC ASPECTS OF FINANCIAL RISK

  1. Thursday, March 3rd, 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.

  2. Sunday, March 6th, 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.

  3. Tuesday, March 8th, 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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