Ruin probability and time of ruin with a proportional reinsurance threshold strategy

Castañer, Anna; Bielsa, M. Mercè Claramunt; Marmol, Maïté Molina

doi:10.1007/s11750-010-0165-5

Cited by 8 publications

(14 citation statements)

References 27 publications

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“…BBOP appears in reinsurance field, and specifically in the analysis of the the effect of reinsurance contracts on the solvency of the two agents that participate in the contract (insurer and reinsurer) [13,19,5,4]. One of the main measures used to control solvency is the ruin probability.…”

Section: Black-box Optimization Problems In Reinsurancementioning

confidence: 99%

“…The final problem tackled in the hardest one, and has been previously tackled in [4]. It consists of minimizing the ultimate ruin probability of the insurer in a threshold proportional reinsurance, i.e.…”

Section: Problem 3: Threshold Proportional Reinsurancementioning

confidence: 99%

“…Instead, the expression of the optimization problem is described, without a final resolution of specific cases [5]. In other cases, numerical results are given, with little explanation of the optimization technique used, or just obtaining optimum values by inspection, whenever this is possible [4].…”

Section: Introductionmentioning

confidence: 99%

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An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

et al. 2013

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Black-box optimization problems (BBOP) are defined as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the field of insurance, and more specifically in reinsurance problems. In this area, the complexity of the models and assumptions considered to define the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, finding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

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Section: Black-box Optimization Problems In Reinsurancementioning

confidence: 99%

Section: Problem 3: Threshold Proportional Reinsurancementioning

confidence: 99%

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An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

et al. 2013

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“…Van Wouwe et al [47] determine the optimal level of excess-loss reinsurance in the case that the ultimate ruin probability is taken as stability criterion. The insurer's survival probability is also considered in [40] and [29], and more recently in [43], [44], [25], [39], [13] and [41]. Guerra and Centeno [28] obtain an optimal reinsurance policy by maximizing the insurer's expected utility.…”

Section: Introductionmentioning

confidence: 99%

Optimal stop-loss reinsurance: a dependence analysis

Castañer

Bielsa

2015

HJMS

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The stop-loss reinsurance is one of the most important reinsurance contracts in the insurance market. From the insurer point of view, it presents an interesting property: it is optimal if the criterion of minimizing the variance of the cost of the insurer is used. The aim of the paper is to contribute to the analysis of the stop-loss contract in one period from the point of view of the insurer and the reinsurer. Firstly, the influence of the parameters of the reinsurance contract on the correlation coefficient between the cost of the insurer and the cost of the reinsurer is studied. Secondly, the optimal stop-loss contract is obtained if the criterion used is the maximization of the joint survival probability of the insurer and the reinsurer in one period.

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“…Instead, the expression of the optimization problem is described, without a final resolution of specific cases [5][6][7][8]. In other cases, numerical results are given, with little explanation of the optimization technique used, or just obtaining optimum values by inspection, whenever this is possible [9].…”

Section: Introductionmentioning

confidence: 99%

Effectively Tackling Reinsurance Problems by Using Evolutionary and Swarm Intelligence Algorithms

Salcedo‐Sanz

Carro-Calvo

Bielsa

et al. 2014

Risks

Self Cite

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This paper is focused on solving different hard optimization problems that arise in the field of insurance and, more specifically, in reinsurance problems. In this area, the complexity of the models and assumptions considered in the definition of the reinsurance rules and conditions produces hard black-box optimization problems (problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program)), which must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in this kind of mathematical problem, so new computational paradigms must be applied to solve these problems. In this paper, we show the performance of two evolutionary and swarm intelligence techniques (evolutionary programming and particle swarm optimization). We provide an analysis in three black-box optimization problems in reinsurance, where the proposed approaches exhibit an excellent behavior, finding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

show abstract

Ruin probability and time of ruin with a proportional reinsurance threshold strategy

Cited by 8 publications

References 27 publications

An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

Optimal stop-loss reinsurance: a dependence analysis

Effectively Tackling Reinsurance Problems by Using Evolutionary and Swarm Intelligence Algorithms

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