Correction

This article refers to:

On a discrete-time risk model with time-dependent claims and impulsive dividend payments

Article title: On a discrete-time risk model with time-dependent claims and impulsive dividend payments

Authors: Lianzeng Zhang and He Liu

Journal: Scandinavian Actuarial Journal

DOI: http://dx.doi.org/10.1080/03461238.2020.1726808

The authors regret to inform the reader that the structural form of ${\Phi }_v\left(u\right)$ has to be adjusted. For $u\in \{b-c,\dots ,b\}$, the identity $\left(\frac{1}{v{q}_i}{\mathcal{B}}^c-\mathcal{J}\right)B_i\left(u\right)=A_i\left(u\right)$ does not hold, and ${\Phi }_v\left(u\right)$ should be treated in the following manner. Since $B_i\left(u\right)=B_i(a-c)$ for $u=b-c,\dots ,b$, it follows from (10) that ${\Phi }_v\left(u\right)={\Phi }_v(a-c)$, $u=b-c,\dots ,b$. Hence, formula (15) should read (15) ${\Phi }_v\left(u\right)=\left\{\begin{array}{ll}{\Phi }_{\mathrm{\infty }}\left(u\right)+\sum _{n=0}^{c\hslash -1}{\kappa }_n{\phi }_n\left(u\right),& u=0,1,\dots ,b-c-1,\\ {\Phi }_v(a-c),& u=b-c,\dots ,b.\end{array}\right.$(15)

Analogously, by noticing the identity ${\text{β}}_i\left(u\right)-{\text{β}}_i(a-c)=v(u+c-a)q_i(1-q_i{)}^{-1}{\tilde{f}}_i(1)$, $u=b-c,\dots ,b$, formula (40) should read (40) $W_v\left(u\right)=\left\{\begin{array}{ll}\sum _{n=0}^{c\hslash -1}{\lambda }_n{\phi }_n\left(u\right),& u=0,1,\dots ,b-c-1,\\ W_v(a-c)+v(u+c-a),& u=b-c,\dots ,b.\end{array}\right.$(40)

Under the above-mentioned modifications, it happens that the numerical results for ${\lambda }_n$'s and $W_v\left(u\right)$ remain unchanged, while the numerical results for ${\kappa }_n$'s and ${\psi }_v\left(u\right)$ are different from the original. As the values of ${\psi }_v\left(u\right)$ in Figures 1(a), 2(a) and 3(a) change slightly, the corresponding observations are still valid. However, the numerical results in Figure 4(a) change a lot (see Table 1 and Figure 1 below). It is shown that a larger value of b corresponds to a larger expected time of ruin, when a is fixed.

Figure 4. Impact of b on ${\psi }_v\left(u\right)$ for a = 20.

Table 5. Numerical results of ${\kappa }_n$'s for a = 20.

	${\kappa }_0$	${\kappa }_1$	${\kappa }_2$	${\kappa }_3$
b = 25	0.04586	0.05046	0.05479	0.05965
b = 30	0.03762	0.04103	0.04495	0.04849
b = 35	0.02955	0.03256	0.03530	0.03848