基于框架对偶投影算法的Gerber-Shiu函数近似计算

In this paper, we consider the ruin problem in the classical compound Poisson model. It is known that the Gerber-Shiu function is one of the most important ruin related functions in ruin theory, and it is very difficult to obtain explicit expression for this function. In this paper, we use the frame duality projection method to compute the Gerber-Shiu function. In stead of approximating the Gerber-Shiu function directly, we first extend this function to the whole real line, and then use frame duality projection to approximate the extended function. Both error analysis is given, and numerical results are also provided to show the effectiveness of the proposed method.??