双边跳扩散过程的首出时和边界分红问题(英文)

First-exit Time and Barrier Strategy of a Jump Diffusion Process with Two-sided Jumps

利用鞅方法讨论了具有正负跳的扩散过程的首出时问题.当上跳服从Erlang(m)分布下跳服从Er-lang(n)分布时,得到了首出的拉普拉斯变换的精确表达式.最后,应用前面的结论解决双指数跳扩散过程的边界分红问题.

The first-exit problem of a jump diffusion process with positive and negative jumps is discussed by the martingale approach.The Laplace transform of the first-exit time is explicitly obtained with the assumption that upward jumps are Erlang（m） distributed and downward ones are Erlang（n） distributed.Finally,by quoting the conclusion obtained as above,expression of the expectation of aggregate dividends until ruin under a barrier strategy is proposed.