CONTINUOUSLY CONTROLLED OPTIONS: DERIVATIVES WITH ADDED FLEXIBILITY

Nikolai Dokuchaev ()
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Nikolai Dokuchaev: Department of Mathematics & Statistics, Curtin University, GPO Box U1987, Perth, 6845 Western Australia, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 01, 1-23

Abstract: The paper introduces special options such that the holder selects dynamically a continuous time process controlling the distribution of the payments (benefits) over time. For instance, the holder can select dynamically the quantity of a commodity purchased or sold by a fixed price given constraints on the cumulative quantity. In a modification of the Asian option, the control process can represent the averaging kernel describing the distribution of the purchases. The pricing of these options requires to solve special stochastic control problems with constraints for the cumulative control similar to a knapsack problem. Some existence results and pricing rules are obtained via modifications of parabolic Bellman equations.

Keywords: Exotic options; controlled options; continuous time market; stochastic control; HJB equation; knapsack problem (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024913500039

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