混合分数跳-扩散模型下一类保底基金的违约概率

摘要

The mixed jump-diffusion fractional Brownian motion model under the Itóformula and fractional diffusion process with non-homogeneous Poisson process is proposed.A special Volterra equations of stochastic differential equations are estimated by discussing the definite solution of the model.Then the explicit solution of the Volterra equations is given by the operator equation iterative method.Finally both the pricing formulas and default probability of the fund with promised lowest return are obtained,and the correlation between the ratio of excess return and the guaranteed return level are also given.%研究了混合跳-扩散分数布朗运动模型下一类分红保底基金的违约概率问题.通过对模型定解问题的讨论得到了一个特殊的Volterra型方程,利用算子方程的迭代法给出了该Volterra型方程的显式解,得到了基金发行公司无法垫资的概率,给出了分红保底基金的定价公式,同时给出了超额收益比例与保底收益水平的相关关系.