Levy processes: Hitting time, overshoot and undershoot II - Asymptotic behaviour
| dc.creator | Roynette, Bernard | |
| dc.creator | Vallois, Pierre | |
| dc.creator | Volpi, Agnes | |
| dc.date | 2005-07-10 | |
| dc.date.accessioned | 2026-07-07T05:21:34Z | |
| dc.date.available | 2026-07-07T05:21:34Z | |
| dc.description | Let (X_t, t>=0) be a Levy process started at 0, with Levy measure nu and T_x the first hitting time of level x>0: T_x:=inf{t>=0; X_t>x}. Let $F(theta, mu, rho,.) be the joint Laplace transform of (T_x, K_x, L_x): F(theta,mu,rho,x) :=E(e^(-theta T_x - mu K_x ρL_x) 1_(T_x<+infinity)), where theta>=0, mu>=0, rho>=0, x>=0, K_x:=X_(T_x)-x and L_x:=x-X_(T_(x^-)). If we assume that nu has finite exponential moments we exhibit an asymptotic expansion for F(theta,mu,rho,x), as x -> +infinity. A limit theorem involving a normalization of the triplet (T_x,K_x,L_x) as x -> +infinity, may be deduced. At last, if nu_(|_R_+) has finite moment of fixed order, we prove that the ruin probability P(T_x<+infinity) has at most a polynomial decay. | |
| dc.description | Manuscript P661 submitted to SPA, October 2004. 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507193 | |
| dc.identifier | http://arxiv.org/abs/math/0507193 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75735 | |
| dc.subject | Probability | |
| dc.title | Levy processes: Hitting time, overshoot and undershoot II - Asymptotic behaviour | |
| dc.type | text |