The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang(2) risk process under constant interest force. An integro-differential equation satisfied by the expected...The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang(2) risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.展开更多
An imbalance between activities of different structures and neurotransmitter systems in the brain is suggested to be the main cause of its abnormal functioning in neurodegenerative pathologies.Electroencephalogram(EE...An imbalance between activities of different structures and neurotransmitter systems in the brain is suggested to be the main cause of its abnormal functioning in neurodegenerative pathologies.Electroencephalogram(EEG)registered from areas specifically linked with a disease in combination with pharmacological testing of involved mediatory systems allows discovery of its progression and mechanism(s). This, in turn, potentiates development of perspective approaches for early diagnostic and effective treatment of neurodegenerative disorders.展开更多
This paper considers the expected discounted penalty function Φ(u) for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the exp...This paper considers the expected discounted penalty function Φ(u) for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ (0) is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.展开更多
In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new stra...In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy (even that of the optimal dividend strategy). Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang (2) and compound Poisson risk models are also given.展开更多
In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy (PCT). Integro-differential equations (IDE) for its Cerber-Shiu functions and dividend payments function are ...In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy (PCT). Integro-differential equations (IDE) for its Cerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations.展开更多
基金supported by the National Natural science Foundation of china(70271069)
文摘The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang(2) risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.
基金Grant RFBR 16-04-00942(Russia)to NB:“A study of the brain dopaminergic system involvement in mechanisms of Alzheimer’s disease on models of its sporadic and inherited types”
文摘An imbalance between activities of different structures and neurotransmitter systems in the brain is suggested to be the main cause of its abnormal functioning in neurodegenerative pathologies.Electroencephalogram(EEG)registered from areas specifically linked with a disease in combination with pharmacological testing of involved mediatory systems allows discovery of its progression and mechanism(s). This, in turn, potentiates development of perspective approaches for early diagnostic and effective treatment of neurodegenerative disorders.
基金Supported by Key Project of National Social Science Fund (Grant No.06&ZD039)"Mathematics+X" Project of DUT
文摘This paper considers the expected discounted penalty function Φ(u) for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ (0) is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.
基金Supported by the National Natural Science Foundation of China (No.10771119)the Research Fund forthe Doctoral Program of Higher Education of China (No.20093705110002)
基金Supported by National Natural Science Foundation of China(Grant No.10871064)Scientific Research Funds of Hu'nan Provincial Education Department(08C883)Hu'nan Provincial Science and Technology Department(2009FJ3141)
文摘In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy (even that of the optimal dividend strategy). Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang (2) and compound Poisson risk models are also given.
基金Supported by the National Basic Research Program of China(973 Program) 2007CB814905the National Natural Science Foundation of China(No.10871102)the Research Fund of the Doctorial Program of Higher Education,the Keygrant Project of Chinese Ministry of Education(No.309009)
文摘In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy (PCT). Integro-differential equations (IDE) for its Cerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations.