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Probability and Math Finance Seminar

Tim Leung

Exponential Hedging with Optimal Stopping in Incomplete Markets

Abstract

We study the problem of hedging American claims with respect to exponential utility within a general incomplete market model. This leads to the construction of a duality formula involving conditional relative entropy minimization and optimal stopping. We further consider claims with multiple exercises, and static-dynamic hedges of American claims with other market-traded European or American options. We will also discuss some applications of this valuation mechanism, including employee stock option (ESO) valuation, and pricing American options on nontraded assets in a regime-switching market. These examples involve analysis of the underlying free-boundary problems, for which we develop a finite-difference numerical scheme to solve for the optimal hedging and exercising strategies. We find that risk-averse investors tend to exercise options early while incorporating static hedges induces delayed exercises.

MONDAY, September 21, 2009
Time: 1:30 P.M.
Location: WeH 6423