The Gerber-Shiu discounted penalty function: A review from practical perspectives
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 …
variety of risk quantities. Ever since its establishment, it has attracted constantly increasing …
An application of fractional differential equations to risk theory
CD Constantinescu, JM Ramirez, WR Zhu - Finance and Stochastics, 2019 - Springer
This paper defines a new class of fractional differential operators alongside a family of
random variables whose density functions solve fractional differential equations equipped …
random variables whose density functions solve fractional differential equations equipped …
On integro-differential algebras
L Guo, G Regensburger, M Rosenkranz - Journal of Pure and Applied …, 2014 - Elsevier
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 …
boundary problems of differential equations. We generalize this concept to that of integro …
Fourier-Cosine Method for Finite-Time Gerber--Shiu Functions
X Li, Y Shi, SC Phillip Yam, H Yang - SIAM Journal on Scientific Computing, 2021 - SIAM
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 …
cosine (COS) method, finite-time Gerber--Shiu functions with the risk process being driven …
[HTML][HTML] Fluctuation theory for level-dependent Lévy risk processes
A level-dependent Lévy process solves the stochastic differential equation d U (t)= d X (t)− ϕ
(U (t)) dt, where X is a spectrally negative Lévy process. A special case is a multi-refracted …
(U (t)) dt, where X is a spectrally negative Lévy process. A special case is a multi-refracted …
On the optimal dividend problem for insurance risk models with surplus-dependent premiums
E Marciniak, Z Palmowski - Journal of Optimization Theory and …, 2016 - Springer
This paper concerns an optimal dividend distribution problem for an insurance company
with surplus-dependent premium. In the absence of dividend payments, such a risk process …
with surplus-dependent premium. In the absence of dividend payments, such a risk process …
Affine storage and insurance risk models
The aim of this paper is to analyze a general class of storage processes, in which the rate at
which the storage level increases or decreases is assumed to be an affine function of the …
which the storage level increases or decreases is assumed to be an affine function of the …
Potential measures for spectrally negative Markov additive processes with applications in ruin theory
The Markov additive process (MAP) has become an increasingly popular modeling tool in
the applied probability literature. In many applications, quantities of interest are represented …
the applied probability literature. In many applications, quantities of interest are represented …
At the edge of criticality: Markov chains with asymptotically zero drift
The main goal of this text is comprehensive study of time homogeneous Markov chains on
the real line whose drift tends to zero at infinity, we call such processes Markov chains with …
the real line whose drift tends to zero at infinity, we call such processes Markov chains with …