Mean-Variance Hedging on uncertain time horizon in a market with a jump

Ngoupeyou, Armand; Lim, Thomas; Kharroubi, Idris

Ngoupeyou, Armand; Lim, Thomas; Kharroubi, Idris (2013), Mean-Variance Hedging on uncertain time horizon in a market with a jump, Applied Mathematics and Optimization, 68, 3, p. 413-444. http://dx.doi.org/10.1007/s00245-013-9213-5

Type

Article accepté pour publication ou publié

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http://hal.archives-ouvertes.fr/hal-00708597

Date

2013

Nom de la revue

Applied Mathematics and Optimization

Volume

Numéro

Éditeur

Springer

Pages

413-444

Résumé (EN)

In this work, we study the problem of mean-variance hedging with a random horizon T ^ tau , where T is a deterministic constant and is a jump time of the underlying asset price process. We rst formulate this problem as a stochastic control problem and relate it to a system of BSDEs with jumps. We then provide a veri cation theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from ltration enlargement theory.

Mots-clés

decomposition in the reference ltration; progressive enlargement of ltration; jump processes; random horizon; Backward SDE; Mean-variance hedging

JEL

G12 - Asset Pricing; Trading Volume; Bond Interest Rates