Singular Stochastic Control and
Applications to Options Theory
in the Presence of Transaction
Costs
Professor Tze Leung Lai
Statistics Department, Stanford University, USA
C.V.
Starr Visiting Professor at HKU
Abstract
We
first give a review of singular stochastic control and its connections, via
viscosity solutions of the Hamilton-Jacobi-Bellman partial differential
equation, to a much simpler optimal stopping problem. We then make use of this
theory to come up with a modification, in the presence of transaction costs, of
the classical Black-Scholes-Merton hedging portfolio
of options, stocks and bonds. In particular, reduction of the associated
singular stochastic control problem to an optimal stopping problem enables us
to develop a relatively simple algorithm to compute the optimal “buy” and
“sell” boundaries in terms of stock prices and time to maturity of the option.
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December 12, 2003 (Friday)
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Room 517, Meng Wah Complex
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Tea
will be held in Room 516, Meng Wah
Complex at 3:40pm