Optimal reinsurance with both proportional and fixed costs

Peng, Li; Zhou, Ming; Yin, Chuancun

doi:10.1016/j.spl.2015.06.024

Cited by 19 publications

(9 citation statements)

References 13 publications

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“…Then the maximal survival probability ( ) given by (6) coincides with Φ. Furthermore, if ( ) * = ( * , * ) satisfies…”

Section: Hjb Integrodifferential and Integral Equationsmentioning

confidence: 95%

“…More recently, taking ruin probability as a risk measure for the insurer, [6] investigated a dynamic optimal reinsurance problem with both fixed and proportional transaction costs for an insurer whose surplus process is modelled by a Brownian motion with positive drift. Under the assumption that the insurer takes noncheap proportional reinsurance, they formulated the problem as a mixed regular control and optimal stopping problem and established that the optimal reinsurance strategy was to never take reinsurance if proportional costs were high and to wait to take the reinsurance when the surplus hits a level.…”

Section: Introductionmentioning

confidence: 99%

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On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

Kasumo

Kasozi

Kuznetsov

2018

Journal of Applied Mathematics

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We consider an insurance company whose reserves dynamics follow a diffusion-perturbed risk model. To reduce its risk, the company chooses to reinsure using proportional or excess-of-loss reinsurance. Using the Hamilton-Jacobi-Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation (VIDE) which we transform into a linear Volterra integral equation (VIE) of the second kind. We then proceed to solve this linear VIE numerically using the block-by-block method for the optimal reinsurance policy that minimizes the ultimate ruin probability for the chosen parameters. Numerical examples with both light- and heavy-tailed distributions are given. The results show that proportional reinsurance increases the survival of the company in both light- and heavy-tailed distributions for the Cramér-Lundberg and diffusion-perturbed models.

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“…Then the maximal survival probability ( ) given by (6) coincides with Φ. Furthermore, if ( ) * = ( * , * ) satisfies…”

Section: Hjb Integrodifferential and Integral Equationsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

Kasumo

Kasozi

Kuznetsov

2018

Journal of Applied Mathematics

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“…Conventional methods, which are based on bandwidth allocation scheme, improve effectively bandwidth utilization efficiency [7,8]. Some methods [9][10][11] achieve real-time data analysis, but they have not considered user investment [12,13], processing cost [14], and the efficient utilization of IoT resources with reduced risks [15,16] of security and robustness [17] issues.…”

Section: Introductionmentioning

confidence: 99%

Processing Optimization of Typed Resources with Synchronized Storage and Computation Adaptation in Fog Computing

Song

Duan

Wan

et al. 2018

Wireless Communications and Mobile Computing

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Wide application of the Internet of Things (IoT) system has been increasingly demanding more hardware facilities for processing various resources including data, information, and knowledge. With the rapid growth of generated resource quantity, it is difficult to adapt to this situation by using traditional cloud computing models. Fog computing enables storage and computing services to perform at the edge of the network to extend cloud computing. However, there are some problems such as restricted computation, limited storage, and expensive network bandwidth in Fog computing applications. It is a challenge to balance the distribution of network resources. We propose a processing optimization mechanism of typed resources with synchronized storage and computation adaptation in Fog computing. In this mechanism, we process typed resources in a wireless-network-based threetier architecture consisting of Data Graph, Information Graph, and Knowledge Graph. The proposed mechanism aims to minimize processing cost over network, computation, and storage while maximizing the performance of processing in a business value driven manner. Simulation results show that the proposed approach improves the ratio of performance over user investment. Meanwhile, conversions between resource types deliver support for dynamically allocating network resources.

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“…However, existing studies on optimal reinsurance mainly focus on the insurance company's interest. See [1], [7], [29], [24], [14], [30], [3], [15], [13], [36], [20], [23], [33], [26], [27], [28], [32], [35].…”

mentioning

confidence: 99%

Optimal stop-loss reinsurance with joint utility constraints

Zhang¹,

Qian²,

Jin³

et al. 2021

Journal of Industrial &Amp; Management Optimization

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We investigate the optimal reinsurance problems in this paper, specifically, the stop-loss strategies that can bring mutual benefit to both the insurance company and the reinsurance company. The utility improvement constraints are adopted by both contracting parties to guarantee that a reinsurance contract will bring higher expected utilities of wealth to the two participants. We also introduce five risk criteria that reflect the interests of both parties. Under each optimality criterion, we obtain explicit expressions of optimal stop-loss retentions and the corresponding optimised value of objective functions. The upper and lower bounds of expected utility increments under the optimal stop-loss retentions are provided. In the numerical example, we analyse the expected utility improvements under the criterion of minimising total Value-at-Risk. Notable increases in the lower bound of total utility increments are observed after adopting the joint utility improvement constraints.

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Optimal reinsurance with both proportional and fixed costs

Cited by 19 publications

References 13 publications

On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

Processing Optimization of Typed Resources with Synchronized Storage and Computation Adaptation in Fog Computing

Optimal stop-loss reinsurance with joint utility constraints

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