Talk Abstract:

Contingent Claims Analysis from an Optimization Viewpoint and A Numerical Method for Computing the Effective Coefficients of Random Media

Lisa Korf
IBM

Consider the problem of a power broker who must price the delivery of power at a contracted price per unit, and also has the ability to produce power to meet customer demands. Such a model can be quite complex, yet the theory of arbitrage pricing in some modified sense should still apply. The classical approach will not suffice to uncover the pricing theory, nor to yield concrete numerical results in this "real-world" setting. When arbitrage pricing theory is cast in an optimization framework, constraints which model such "real" problems may be added, and conjugate duality exploited to uncover the modified fundamental theory of arbitrage pricing that may in turn be used to price these contracts. This talk presents a continuous time arbitrage pricing model, and develops the corresponding pricing theory in a flexible and computationally attractive optimization setting. (Joint with Alan King)

Environmental models must constantly deal with composite materials (soils, etc.) whose make-up is not fully known. Stochastic partial differential equations often arise, but are difficult to apply because they contain random coefficients. These coefficients may in practice be replaced with "effective" deterministic ones which still capture the essential behavior of the material in question. Computing such effective coefficients is therefore a topic of great interest. This talk focuses on the development of a numerical procedure for the computation of effective coefficients of random media, based on sampling from a stationary distribution. The consistency of the empirical estimates is proven through a specialized ergodic theorem and the techniques of variational analysis. (Joint with with Roger Wets)

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