On the discrete-time compound renewal risk model with dependence

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

“…Recursive methods were successfully analysed in many diverse fields, ranging from queuing models (Ferreira et al, 2017) to dynamical systems (De La Sen, 2016). Various properties of the Gerber-Shiu function in the discrete time risk models were considered by Bao and Liu (2016), Cheng et al (2000), Li and Wu (2015), Li (2005), Li and Garrido (2002), Li et al (2009), Liu et al (2017), Liu and Guo (2006), Marceau (2009), Pavlova and Willmot (2004). For instance, in Li and Garrido (2002), it is shown that values of function δ,w of the homogeneous discrete time risk model can be calculated using the following formulas…”

On two families of bivariate distributions with exponential marginals: Aggregation and capital allocation

“…in Joe (1997) and as illustrated e.g. in Denuit et al (2005), Cossette et al (2002), and Genest et al (2003), Trivedi and Zimmer (2005) and Marceau (2009). This type of structure permits the coupling of various marginals.…”

The Gerber-Shiu Expected Penalty Function for the Risk Model with Dependence and a Constant Dividend Barrier

“…and p.d.f. given by (6) and 7, respectively. In particular, we know from (7) that the conditional p.d.f.…”

“…In Boudreault et al [5], a risk model with time-dependent claim sizes (i.e., the distribution of the next claim size depends on the last interarrival time) is analyzed and a defective renewal equation for the Gerber-Shiu discounted penalty function is derived and solved. Marceau [6] has considered the discrete-time renewal risk model with dependence between the claim amount random variable and the interclaim time random variable. Recursive formulas are derived for the probability mass function and the moments of the total claim amount over a fixed period of time.…”