course: Convex Duality In Probability, Mathematical Statistics, And Finance

speaker: Ioannis Karatzas (Columbia University)

abstract: Methods from Convex Analysis and Duality can be used to great effect in many fields. We shall provide in these Lectures an overview of what can be accomplished by using such techniques in the following contexts:

. The Least-Squares Approximation of Random Variables by Stochastic Integrals.

. The classical problem of Hypothesis Testing in Mathematical Statistics.

. The problem of Expected Utility Maximization in Mathematical Economics.

. The problems of Super-Replication, Reaching a Goal with maximal probability, and Partial Hedging, in the Mathematics of Finance.

RECOMMENDED TEXT:

I. KARATZAS (1996) Lectures on the Mathematics of Finance. CRM Monographs Volume 8, 148 pp. American Mathematical Society, Providence, Rhode Island.

RECOMMENDED BIBLIOGRAPHY:

J. CVITANIC & I. KARATZAS (1999) On dynamic measures of risk. Finance & Stochastics 3, 451-482.

J. CVITANIC & I. KARATZAS (2001) Generalized Neyman-Pearson lemma via convex duality. Bernoulli 7, 79-97.

J. DETEMPLE & I. KARATZAS (2001) Non-addictive habits: optimal portfolio-consumption policies. Preprint.

Ch. HOU & I. KARATZAS (2001) On the least-squares approximation of random variables by stochastic integrals. Preprint.

I. KARATZAS & G. ZITKOVIC (2001) Optimal consumption from investment and random endowment in incomplete semi-martingale markets. Preprint.

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