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American options, multi-armed bandits, and optimal consumption plans: a unifying view. (English) Zbl 1065.91022

Carmona, René A. (ed.) et al., Paris-Princeton lectures on mathematical finance 2002. Berlin: Springer (ISBN 3-540-40193-8/pbk). Lect. Notes Math. 1814, 1-42 (2003).
The authors show that various stochastic optimization problems arising in the option theory, in dynamical allocation problems, and in the microeconomic theory of intertemporal consumption choice can be reduced to the same problem of the representation of a given stochastic process in terms of running maxima of another process. This stochastic representation provides a new method for solving such problems. The general solution of the stochastic representation problem is presented. Explicit solutions to the representation problem in homogeneous situations where randomness is generated by a Lévy process or by a one-dimensional diffusion, are derived. The authors present an algorithm which explicitly solves the discrete-time version of the general representation problem.
For the entire collection see [Zbl 1018.00007].

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B16 Utility theory
60G40 Stopping times; optimal stopping problems; gambling theory
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