TY - JOUR
T1 - Optimal Dividend Strategy Under Parisian Ruin with Affine Penalty
AU - Xu, Ran
AU - Wang, Wenyuan
AU - Garrido, Jose
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/5/10
Y1 - 2021/5/10
N2 - In this paper, we investigate the optimal dividend problem under Parisian ruin with affine penalty payments at Parisian ruin time. The underlying risk process is assumed to be a spectrally negative Lévy risk process. With the help of the dynamic programming principle, we prove that the value function associated to our optimal control problem is the smallest solution with certain characteristics to the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, the form of the performance function under barrier dividend strategy is expressed in terms of various extended scale functions. Then we identify a condition under which the performance function under certain barrier strategy is also a solution to the HJB equation, which in turn illustrates the optimalilty of such barrier dividend strategy among all admissible strategies. Various numerical examples are also given when the underlying risk process is compound Poisson process, Brownian motion with drift and jump-diffusion process.
AB - In this paper, we investigate the optimal dividend problem under Parisian ruin with affine penalty payments at Parisian ruin time. The underlying risk process is assumed to be a spectrally negative Lévy risk process. With the help of the dynamic programming principle, we prove that the value function associated to our optimal control problem is the smallest solution with certain characteristics to the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, the form of the performance function under barrier dividend strategy is expressed in terms of various extended scale functions. Then we identify a condition under which the performance function under certain barrier strategy is also a solution to the HJB equation, which in turn illustrates the optimalilty of such barrier dividend strategy among all admissible strategies. Various numerical examples are also given when the underlying risk process is compound Poisson process, Brownian motion with drift and jump-diffusion process.
KW - Affine penalty payments
KW - Optimal dividend problem
KW - Parisian ruin
KW - Spectrally negative Lévy process
UR - http://www.scopus.com/inward/record.url?scp=85105552438&partnerID=8YFLogxK
U2 - 10.1007/s11009-021-09865-7
DO - 10.1007/s11009-021-09865-7
M3 - Article
AN - SCOPUS:85105552438
SN - 1387-5841
VL - 24
SP - 1385
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 3
ER -