Zhibin Liang

Nanjing Normal University

Mathematical optimizationCompound Poisson processReinsuranceStochastic controlMathematics

19Publications

9H-index

289Citations

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Publications 19

Newest

#1Xiaoqing Liang (HEBUT: Hebei University of Technology)H-Index: 3

#2Zhibin Liang (Nanjing Normal University)H-Index: 9

Last. Virginia R. Young (UM: University of Michigan)H-Index: 28

view all 3 authors...

We consider the problem of minimizing the probability of ruin by purchasing reinsurance whose premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We derive closed-form expressions of the optimal reinsurance strategy and the corresponding minimum probability of ruin under the diffusion approximation of the classical Cram\'er-Lundberg risk process perturbed by a diffusion. We find an explicit expression for the ...

Optimal reinsurance to minimize the probability of drawdown under the mean-variance premium principle

#1Xia Han (Nanjing Normal University)H-Index: 1

#2Zhibin Liang (Nanjing Normal University)H-Index: 9

Last. Virginia R. Young (UM: University of Michigan)H-Index: 28

view all 3 authors...

In this paper, we determine the optimal reinsurance strategy to minimize the probability of drawdown, namely, the probability that the insurer's surplus process reaches some fixed fraction of its m...

#1Xiaoqing Liang (HEBUT: Hebei University of Technology)H-Index: 3

#2Zhibin Liang (Nanjing Normal University)H-Index: 9

Last. Virginia R. Young (UM: University of Michigan)H-Index: 28

view all 3 authors...

Abstract We consider the problem of minimizing the probability of ruin by purchasing reinsurance whose premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We derive closed-form expressions of the optimal reinsurance strategy and the corresponding minimum probability of ruin under the diffusion approximation of the classical Cramer-Lundberg risk process perturbed by a diffusion. We find an explicit expression f...

Optimal proportional reinsurance with common shock dependence to minimise the probability of drawdown

#1Xia Han (Nanjing Normal University)H-Index: 1

#2Zhibin Liang (Nanjing Normal University)H-Index: 9

Last. Caibin Zhang (Nanjing Normal University)H-Index: 1

view all 3 authors...

In this paper, we study the optimal proportional reinsurance problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component, and the criterion is to minimise the probability of drawdown, namely, the probability that the value of the surplus process reaches some fixed proportion of its maximum value to date. By the method of maximising the ratio of drift of a diffusion divided to its volatility squared...

#1Zhibin Liang (Nanjing Normal University)H-Index: 9

#2Virginia R. Young (UM: University of Michigan)H-Index: 28

We find the optimal dividend strategy in two related risk models under an affine penalty for ruin. The first risk model is the classical Cramer–Lundberg risk model, and the second is the so-called dual risk model. Under both models, for exponentially distributed jumps, we show that the optimal dividend strategy is a barrier strategy and obtain the barrier explicitly. Moreover, we prove that the optimal barrier increases with respect to the parameters of the affine penalty, while the penalized va...

#1Caibin Zhang (Nanjing Normal University)H-Index: 2

#2Zhibin Liang (Nanjing Normal University)H-Index: 9

Last. Kam Chuen Yuen (HKU: University of Hong Kong)H-Index: 22

view all 3 authors...

This paper studies an optimal dynamic proportional reinsurance in a risk model with two dependent classes of insurance business. Under the criterion of maximizing the mean–variance utility of the t...

#1Junna Bi (ECNU: East China Normal University)H-Index: 5

#2Zhibin Liang (Nanjing Normal University)H-Index: 9

Last. Kam Chuen Yuen (HKU: University of Hong Kong)H-Index: 22

view all 3 authors...

In this paper, we consider the problem of optimal investment-reinsurance with two dependent classes of insurance risks in a regime-switching financial market. In our model, the two claim-number processes are correlated through a common shock component, and the market mode is classified into a finite number of regimes. We also assume that the insurer can purchase proportional reinsurance and invest its surplus in a financial market, and that the values of the model parameters depend on the market...

Optimal proportional reinsurance to minimize the probability of drawdown under thinning-dependence structure

#1Xia Han (Nanjing Normal University)H-Index: 1

#2Zhibin Liang (Nanjing Normal University)H-Index: 9

Last. Kam Chuen Yuen (HKU: University of Hong Kong)H-Index: 22

view all 3 authors...

AbstractIn this paper, we consider the optimal proportional reinsurance problem in a risk model with the thinning-dependence structure, and the criterion is to minimize the probability that the val...

#1Wei Wei (HKU: University of Hong Kong)H-Index: 21

#1Wei Wei (HKU: University of Hong Kong)

Last. Kam Chuen Yuen (HKU: University of Hong Kong)H-Index: 22

view all 3 authors...

This paper considers the problem of optimal reinsurance in a compound Poisson risk model with dependent classes of insurance business. It is assumed that the risk process in each class follows a compound Poisson process, and that all classes are correlated due to the so-called thinning-dependence structure. Under the criterion of maximizing the adjustment coefficient, methods for finding the optimal reinsurance strategies are discussed for both the expected value premium principle and the varian...

Optimal reinsurance and investment in a jump-diffusion financial market with common shock dependence

#1Zhibin Liang (Nanjing Normal University)H-Index: 9

#2Kam Chuen Yuen (HKU: University of Hong Kong)H-Index: 22

Last. Caibin Zhang (Nanjing Normal University)H-Index: 2

view all 3 authors...

In this paper, we study the optimal reinsurance and investment problem in a financial market with jump-diffusion risky asset. It is assumed that the insurance risk model is modulated by a compound Poisson process, and that the jumps in both the risky asset and insurance risk process are correlated through a common shock. Under the criterion of maximizing the expected exponential utility, we adopt a nonstandard approach to examine the existence and uniqueness of the optimal strategy. Using the te...

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