The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an...The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly.The claim process of the insurer is governed by a Brownian motion with a drift.A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle.Both the insurer and the reinsurer are assumed to invest in a risky asset,which is distinct for each other and driven by a constant elasticity of variance model.The optimal decision is formulated on a weighted sum of the insurer’s and the reinsurer’s surplus processes.Upon a verification theorem,which is established with a formal proof for a more general problem,explicit solutions are obtained for the proposed investment-reinsurance model.Moreover,numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.展开更多
Mean-variance relationship （MVR）, nowadays agreed in power law form, is an important function. It is currently used by traffic matrix estimation as a basic statistical assumption. Because all the existing papers obt...Mean-variance relationship （MVR）, nowadays agreed in power law form, is an important function. It is currently used by traffic matrix estimation as a basic statistical assumption. Because all the existing papers obtain MVR only through empirical ways, they cannot provide theoretical support to power law MVR or the definition of its power exponent. Furthermore, because of the lack of theoretical model, all traffic matrix estimation methods based on MVR have not been theoretically supported yet. By observing both our laboratory and campus network for more than one year, we find that such an empirical MVR is not sufficient to describe actual network traffic. In this paper, we derive a theoretical MVR from ON/OFF model. Then we prove that current empirical power law MVR is generally reasonable by the fact that it is an approximate form of theoretical MVR under specific precondition, which can theoretically support those traffic matrix estimation algorithms of using MVR. Through verifying our MVR by actual observation and public DECPKT traces, we verify that our theoretical MVR is valid and more capable of describing actual network traffic than power law MVR.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11301376, 71201173 and 71571195)China Scholarship Council, the Natural Sciences and Engineering Research Council of Canada (NSERC)+2 种基金Society of Actuaries Centers of Actuarial Excellence Research Grant, Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2015A030306040)Natural Science Foundation of Guangdong Province of China (Grant No. 2014A030310195)for Ying Tung Eduction Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 151081)
文摘The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly.The claim process of the insurer is governed by a Brownian motion with a drift.A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle.Both the insurer and the reinsurer are assumed to invest in a risky asset,which is distinct for each other and driven by a constant elasticity of variance model.The optimal decision is formulated on a weighted sum of the insurer’s and the reinsurer’s surplus processes.Upon a verification theorem,which is established with a formal proof for a more general problem,explicit solutions are obtained for the proposed investment-reinsurance model.Moreover,numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.
基金Supported by the National Basic Research Program of China (Grant No. G2005CB321901)
文摘Mean-variance relationship （MVR）, nowadays agreed in power law form, is an important function. It is currently used by traffic matrix estimation as a basic statistical assumption. Because all the existing papers obtain MVR only through empirical ways, they cannot provide theoretical support to power law MVR or the definition of its power exponent. Furthermore, because of the lack of theoretical model, all traffic matrix estimation methods based on MVR have not been theoretically supported yet. By observing both our laboratory and campus network for more than one year, we find that such an empirical MVR is not sufficient to describe actual network traffic. In this paper, we derive a theoretical MVR from ON/OFF model. Then we prove that current empirical power law MVR is generally reasonable by the fact that it is an approximate form of theoretical MVR under specific precondition, which can theoretically support those traffic matrix estimation algorithms of using MVR. Through verifying our MVR by actual observation and public DECPKT traces, we verify that our theoretical MVR is valid and more capable of describing actual network traffic than power law MVR.
