In this paper, the surplus process of the insurance company is described by a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and purchase excess-of-lo...In this paper, the surplus process of the insurance company is described by a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and purchase excess-of-loss reinsurance. Under short-selling prohibition, we consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the probability of ruin. We first show that the excess-of-loss reinsurance strategy is always better than the proportional reinsurance under two objective functions. Then, by solving the corresponding Hamilton-Jacobi-Bellman equations, the closed-form solutions of their optimal value functions and the corresponding optimal strategies are obtained. In particular, when there is no risky-free interest rate, the results indicate that the optimal strategies, under maximizing the expected exponential utility and minimizing the probability of ruin, are equivalent for some special parameter. This validates Ferguson's longstanding conjecture about the relation between the two problems.展开更多
In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distributi...In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.展开更多
An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is...An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.展开更多
Extensive indoor channel measurements were conducted in Beijing with wideband multiple-input multiple-output （MIMO） sounder at 5.25 GHz. Both line-of-sight （LOS） and non-line-of-sight （NLOS） propagation were mea...Extensive indoor channel measurements were conducted in Beijing with wideband multiple-input multiple-output （MIMO） sounder at 5.25 GHz. Both line-of-sight （LOS） and non-line-of-sight （NLOS） propagation were measured in the indoor office and hotspot scenarios. On the basis of measured data, statistical channel characteristics are presented in this article, including the empirical path loss （PL） models, three excess delay parameters, circular azimuth spread （CAS）, and circular elevation spread （CES）. Comparative analysis of different propagation mechanisms in two scenarios is conducted. These values are significant for indoor coverage and technical research of MIMO and orthogonal frequency division multiplexing （OFDM） for the international mobile telecommunications-advanced （IMT-Advanced） system.展开更多
This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and...This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.展开更多
基金supported by Keygrant Project of Ministry of Education, China (Grant No. 309009)National Natural Science Foundation of China (Grant No. 10871102)
文摘In this paper, the surplus process of the insurance company is described by a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and purchase excess-of-loss reinsurance. Under short-selling prohibition, we consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the probability of ruin. We first show that the excess-of-loss reinsurance strategy is always better than the proportional reinsurance under two objective functions. Then, by solving the corresponding Hamilton-Jacobi-Bellman equations, the closed-form solutions of their optimal value functions and the corresponding optimal strategies are obtained. In particular, when there is no risky-free interest rate, the results indicate that the optimal strategies, under maximizing the expected exponential utility and minimizing the probability of ruin, are equivalent for some special parameter. This validates Ferguson's longstanding conjecture about the relation between the two problems.
基金supported by the National Key R&D Program of China(2022YFA1007900)the National Natural Science Foundation of China(Nos.12271171,12171158,12071147,12001200)+3 种基金the Shanghai Philosophy Social Science Planning Office Project(Grant No.2022ZJB005)the Fundamental Research Funds for the Central Universities(2022QKT001)the State Key Program of National Natural Science Foundation of China(71931004)the Humanity and Social Science Foundation of Ningbo University(XPYB19002)。
文摘In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.
基金National Natural Science Foundation of China(No.62073071)Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University,China(No.CUSF-DH-D-2021045)。
文摘An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.
基金the Hi-Tech Research and Development Program of China (2006AA01Z258), China Mobile Research Institute
文摘Extensive indoor channel measurements were conducted in Beijing with wideband multiple-input multiple-output （MIMO） sounder at 5.25 GHz. Both line-of-sight （LOS） and non-line-of-sight （NLOS） propagation were measured in the indoor office and hotspot scenarios. On the basis of measured data, statistical channel characteristics are presented in this article, including the empirical path loss （PL） models, three excess delay parameters, circular azimuth spread （CAS）, and circular elevation spread （CES）. Comparative analysis of different propagation mechanisms in two scenarios is conducted. These values are significant for indoor coverage and technical research of MIMO and orthogonal frequency division multiplexing （OFDM） for the international mobile telecommunications-advanced （IMT-Advanced） system.
基金the National Natural Science Foundation of China(19831020,10471008)
文摘This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.
