On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation

On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes

“…For the study of ruin-related quantities in dependent Sparre Andersen models under specific distributional assumptions on the interclaim time V and/or the claim severity Y , we refer interested readers to e.g. Boudreault et al (2006), Cossette et al (2008Cossette et al ( , 2010, Ambagaspitiya (2009), Badescu et al (2009), Chadjiconstantinidis and Vrontos (2012), Willmot and Woo (2012), Zhang et al (2012), and Landriault et al (2013). In this paper, we are mostly concerned with the dependency structure proposed by Willmot and Woo (2012), who assumed that the joint density of the generic pair (V, Y ) at (t, y) admits the factorization form…”

The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

“…For instance, several cases of the Sparre Andersen model were considered by Dickson and Qazvini (2016), Landriault and Willmot (2008), Li and Garrido (2004), Li and Sendova (2015), Lin et al (2003), Schmidli (1999), Willmot and Dickson (2003). Properties of the Gerber-Shiu function in the risk renewal models perturbed by diffusion were investigated by Chi et al (2010), Tsai (2003), Tsai and Willmot (2002), Xu et al (2014), Zhang and Cheung (2016), Zhang et al (2012Zhang et al ( , 2017bZhang et al ( , 2014. The Gerber-Shiu function of the risk models with various special strategies were considered by Avram et al (2015), Bratiichuk (2012), Cheung and Liu (2016), Cheung et al (2015), Dong et al (2009), Lin and Pavlova (2006), Lin and Sendova (2008), Liu et al (2015), Marciniak and Palmowski (2016), Shi et al (2013), Shiraishi (2016), Woo et al (2017), Zhang et al (2017a), Zhou et al (2015).…”

The Gerber-Shiu discounted penalty function: A review from practical perspectives

“…As for the claim size, one finds models with arbitrary interclaim time distribution and a Coxian claim-size distribution [96], and phase-type interclaim times and claim-size distributions in the rational family [150] with an additional multi-layer dividend strategy [79]. Additional features have been introduced into the risk model, such as dependent interclaim times and claim amounts with perturbation [199], stochastic premium income [201], stochastic interest force modeled by drifted Brownian model in combination with Poisson-Geometric process [72], and two classes of claims modelled by compound Poisson and Erlang(2) renewal risk processes with a two-step premium rate under a threshold dividend strategy [121].…”

“…Defective renewal equations can be found for the compound binomial model [93] and for a general Sparre-Andersen model with both positive and negative claim values [91]. Renewal type equations are derived even when additional structural features are introduced, for example, a Sparre-Andersen model involving a multi-layer dividend policy [180], random claims or income modeled by a compound Poisson process [29,201] along with perturbation and dependence between interclaim times and claim amounts [199], a two-step premium rate under a threshold dividend strategy [121], and a stochastic discount rate modeled by a Brownian motion and a Poisson-Geometric process [72]. Defective renewal equations are derived for variants of the Gerber-Shiu function driven by a Sparre-Andersen process, such as (2.10) with general interclaim times [35], the formulation (2.11) with Coxian-distributed interclaim times and mixed Erlang-distributed claim amounts [170] or with two-sided jumps [195], and the formulation (2.13) with dependent interclaim times and claim sizes [40].…”