We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterise its three coefficient processes as solutions of semimartingale backward stochastic differential equations and show how they can be used to describe the optimal trading strategy for each conditional mean-variance hedging problem. For comparison with the existing literature, we provide alternative equivalent versions of the BSDEs and present a number of simple examples.
Mean-variance hedging via stochastic control and BSDEs for general semimartingales / Jeanblanc, M.; Mania, M.; Santacroce, Marina; Schweizer, M.. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - STAMPA. - 22:6(2012), pp. 2388-2428. [10.1214/11-AAP835]
Mean-variance hedging via stochastic control and BSDEs for general semimartingales
SANTACROCE, MARINA;
2012
Abstract
We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterise its three coefficient processes as solutions of semimartingale backward stochastic differential equations and show how they can be used to describe the optimal trading strategy for each conditional mean-variance hedging problem. For comparison with the existing literature, we provide alternative equivalent versions of the BSDEs and present a number of simple examples.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2502248
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