Convex bounds on multiplicative processes, with applications to pricing in incomplete markets

Courtois, Cindy;Denuit, Michel
(2008) Insurance: Mathematics and Economics — Vol. 42, n° 1, p. 95-100 (2008)

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Extremal distributions have been extensively used in the actuarial literature in order to derive bounds on functionals of the underlying risks, such as stop-loss premiums or ruin probabilities, for instance. In this paper, the idea is extended to a dynamic setting. Specifically, convex bounds on multiplicative processes are derived. Despite their relative simplicity, the extremal processes are shown to produce reasonably accurate bounds on option prices in the classical trinomial model for incomplete markets. (C) 2007 Elsevier B.V. All rights reserved.
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Courtois, C., & Denuit, M. (2008). Convex bounds on multiplicative processes, with applications to pricing in incomplete markets. Insurance: Mathematics and Economics, 42(1), 95-100. https://doi.org/10.1016/j.insmatheco.2007.01.013 (Original work published 2008)