Abstract The Gerber-Shiu function provides a unified framework for the evaluation of a
variety of risk quantities. Ever since its establishment, it has attracted constantly increasing …

This paper defines a new class of fractional differential operators alongside a family of
random variables whose density functions solve fractional differential equations equipped …

The concept of integro-differential algebra has been introduced recently in the study of
boundary problems of differential equations. We generalize this concept to that of integro …

In this paper, we provide three equivalent expressions for ruin probabilities in a Cramér–
Lundberg model with gamma distributed claims. The results are solutions of integro …

In this article, we provide the first systematic numerical study on, via the popular Fourier-
cosine (COS) method, finite-time Gerber--Shiu functions with the risk process being driven …

We review our algebraic framework for linear boundary problems (concentrating on ordinary
differential equations). Its starting point is an appropriate algebraization of the domain of …

In this article, we provide a systematic study on effectively approximating the Gerber–Shiu
functions, which is a hardly touched topic in the current literature, by incorporating the …

In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin
probabilities and discounted penalty functions in renewal insurance risk models when the …

We consider a renewal jump–diffusion process, more specifically a renewal insurance risk
model with investments in a stock whose price is modeled by a geometric Brownian motion …

The seminal paper by Gerber and Shiu (1998) unified and extended the study of the event of
ruin and related quantities, including the time at which the event of ruin occurs, the deficit at …