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On the central management of risk networks

Part of: Stochastic processes Special processes Markov processes

Published online by Cambridge University Press:  17 March 2017

Florin Avram  and
Andreea Minca
Florin Avram*
Affiliation:
Université de Pau
Andreea Minca*
Affiliation:
Cornell University
*
* Postal address: Département de Mathématiques, Université de Pau, Pau 64000, France. Email address: florin.avram@univ-pau.fr
** Postal address: School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14850, USA. Email address: acm299@cornell.edu
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Abstract

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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.

Keywords

Multidimensional risk processSparre Andersen processMarkov additive processmatrix exponential approximationruin probability

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60J75: Jump processes
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 1 , March 2017 , pp. 221 - 237
Copyright
Copyright © Applied Probability Trust 2017 

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