On the central management of risk networks. (17th March 2017)

• Record Type: Journal Article
• Authors: Avram, Florin; Minca, Andreea
• Is Part Of: Advances in applied probability. Volume 49:Number 1(2017)
• Page Start: 221
• Page End: 237
• Publication Date: 2017-03-17
• Subjects: Multidimensional risk process, -- Sparre Andersen process, -- Markov additive process, -- matrix exponential approximation, -- ruin probability; Primary 60G51, -- Secondary 60K30, -- 60J75; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.85
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: In this paper we identify three questions concerning the management of risk networks with a central branch, which may be solved using the extensive machinery available for one-dimensional risk models. First, we propose a criterion for judging whether a subsidiary is viable by its readiness to pay dividends to the central branch, as reflected by the optimality of the zero-level dividend barrier. Next, for a deterministic central branch which must bailout a single subsidiary each time its surplus becomes negative, we determine the optimal bailout policy, as well as the ruin probability and other risk measures, in closed form. Moreover, we extend these results to the case of hierarchical networks. Finally, for nondeterministic central branches with one subsidiary, we compute approximate risk measures by applying rational approximations, and by using the recently developed matrix scale methodology.