Motivé par des considérations classiques de la théorie du risque, nous étudions des problèmes de croisement de frontière par des processus de Lévy réfractés. Un processus de Lévy réfracté est un processus de Lévy dont la dynamique possède une dérive linéaire fixe. Plus formellement, un processus de Lévy réfracté est décrit par l'unique solution forte, si elle existe, de l'équation différentielle stochastique
Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation
Mots clés : stochastic control, fluctuation theory, Lévy processes
@article{AIHPB_2010__46_1_24_0, author = {Kyprianou, A. E. and Loeffen, R. L.}, title = {Refracted {L\'evy} processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {24--44}, publisher = {Gauthier-Villars}, volume = {46}, number = {1}, year = {2010}, doi = {10.1214/08-AIHP307}, mrnumber = {2641768}, zbl = {1201.60042}, language = {en}, url = {http://www.numdam.org/articles/10.1214/08-AIHP307/} }
TY - JOUR AU - Kyprianou, A. E. AU - Loeffen, R. L. TI - Refracted Lévy processes JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2010 SP - 24 EP - 44 VL - 46 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/08-AIHP307/ DO - 10.1214/08-AIHP307 LA - en ID - AIHPB_2010__46_1_24_0 ER -
Kyprianou, A. E.; Loeffen, R. L. Refracted Lévy processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 1, pp. 24-44. doi : 10.1214/08-AIHP307. http://www.numdam.org/articles/10.1214/08-AIHP307/
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