Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

Abstract

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.

Risk, Ruin and Survival

“…Finally, Lkabous and Renaud (2018) perform a sensitivity analysis of their risk measure in the case of a Cramér-Lundberg process with exponential claims. Loke and Thomann (2018):…”

“…In greater generality, many subsequent risk models have also incorporated investments with constant force of interest, which could be, e.g., investments of the entire surplus in bonds, as earlier argued by . These arguments have motivated Loke and Thomann (2018) to further explore the problems in detail, particularly from the view of practical implementation needs, such as speedy decision making for which numerical algorithms become indispensable. Hence, the authors have put forward and examined the performance of a numerical algorithm for tackling the ruin probability in the dual risk model with risk-free investments under arbitrary gain distributions.…”

Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”

“…In greater generality, many subsequent risk models have also incorporated investments with constant force of interest, which could be, e.g., investments of the entire surplus in bonds, as earlier argued by Segerdahl (1942). These arguments have motivated Loke and Thomann (2018) to further explore the problems in detail, particularly from the view of practical implementation needs, such as speedy decision making for which numerical algorithms become indispensable. Hence, the authors have put forward and examined the performance of a numerical algorithm for tackling the ruin probability in the dual risk model with risk-free investments under arbitrary gain distributions.…”

“…Crucially for the algorithm, the ruin probability has been shown to satisfy an integro-differential equation, which the authors subsequently discretized and reduced to a linear matrix equation. This has enabled Loke and Thomann (2018) to efficiently compute the ruin probability for any jump distribution. Furthermore, the authors have employed an analogous numerical method to tackle other Gerber-Shiu type functions, such as the Laplace transform of the time of ruin.…”

Recurrent Sequences Play for Survival Probability of Discrete Time Risk Model

“…Since 1957, when the Sparre Andersen's risk model (1) was introduced, there occurred a significant amoutn of research papers across the world on certain versions of the model (1). For example, [2][3][4][5][6][7][8][9][10][11][12] and many others. An observable break in the subject was achieved when [7,13,14] were published in 1988.…”