Ji, Lanpeng
Robert, Stephan
Ruin problem of a two-dimensional fractional Brownian motion risk process
Stochastic Models
Stochastic Models
Stochastic Models
Stochastic Models
24 p.
asymptotics
fractional Brownian motion
reinsurance
ruin probability
ruin time
two-dimensional risk process
primary 60G15
secondary 60G70
IngĂ©nierie
2018
2018-01
This paper investigates ruin probability and ruin time of a two-dimensional fractional Brownian motion risk process. The net loss process of an insurance company is modeled by a fractional Brownian motion. The two-dimensional fractional Brownian motion risk process models the surplus processes of an insurance and a reinsurance company, where the net loss is divided between them in some specified proportions. The ruin problem considered is that of the two-dimensional risk process first entering the negative quadrant, that is, the simultaneous ruin problem. We derive both asymptotics of the ruin probability and approximations of the scaled conditional ruin time as the initial capital tends to infinity.
1532-6349
Stochastic Models
10.1080/15326349.2017.1389284
English