On finite-time ruin probabilities in a generalized dual risk model with dependence

Abstract

Citation: Dimitrova, D. S., Kaishev, V. K. and Zhao, S. (2015). On finite-time ruin probabilities in a generalized dual risk model with dependence. European Journal of Operational Research, 242(1), pp. 134-148. doi: 10.1016Research, 242(1), pp. 134-148. doi: 10. /j.ejor.2014 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this paper, we study the finite-time ruin probability in a reasonably generalized dual risk model, where we assume any non-negative non-decreasing cumulative operational cost function and arbitrary capital gains arrival process. Establishing an enlightening link between this dual risk model and its corresponding insurance risk model, explicit expressions for the finite-time survival probability in the dual risk model are obtained under various general assumptions for the distribution of the capital gains. In order to make the model more realistic and general, different dependence structures among capital gains and inter-arrival times and between both are also introduced and corresponding ruin probability expressions are also given. The concept of alarm time, as introduced in Das and Kratz (2012), is applied to the dual risk model within the context of risk capital allocation. Extensive numerical illustrations are provided.

Duality in ruin problems for ordered risk models

“…Theorem 5.1 compares with Proposition 2.2 obtained by Dimitrova et al [18] for another dual risk model in which the profit arrival process is arbitrary and the profit sizes are linear combinations of independent exponentials.…”

“…In all cases, the formulas have a clear algebraic structure and can be used for numerical computation. Some illustrations for simpler variants of these models can be found, e.g., in Goffard and Lefèvre [23] and Dimitrova et al [18]. Of course, other ruin topics could be studied by a similar duality approach.…”

“…First-passage problems and ruin time are also much studied; see e.g. Landriault and Sendova [26], Mazza and Rullière [31], Zhu and Yang [43], Yang and Sendova [42] and Dimitrova et al [18]. There exists here a close and important connection with queueing models; see e.g.…”

“…Let us mention e.g. the recent papers by Shi and Landriault [39], Mazza and Rullière [31], Borovkov and Dickson [10] and Dimitrova et al [18]. A similar duality property is used with Lévy processes in finance.…”

“…Picard and Lefèvre [33], Loisel and Rullière [36] and Lefèvre and Loisel [27]) and then pass to the insurance model with exponential claim amounts. Dimitrova et al [18] apply results for the insurance model to obtain the ruin probability in the corresponding dual model.…”