On PBIL, DE and PSO for Optimization of Reinsurance Contracts

Cortes, Omar Andrés Carmona; Rau-Chaplin, Andrew; Wilson, Duane; Gaiser-Porter, Jürgen

doi:10.1007/978-3-662-45523-4_19

Cited by 9 publications

(3 citation statements)

References 11 publications

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“…In the original version of the algorithm, the population were encoded using binary vectors and an associated probability vector, which was then updated based on the best members of a population. Unlike other evolutionary algorithms, a new population is generated at random using the updated probability vector for each generation [13]. Since Baluja's initial work, extensions to the algorithm have been proposed for continuous and base-n represented search spaces [14], [15].…”

Section: Multiobjective Fundamentalsmentioning

confidence: 99%

A new vector evaluated PBIL algorithm for reinsurance analytics

Cortes

Rau-Chaplin

Prado

2015

2015 Latin America Congress on Computational Intelligence (LA-CCI)

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The purpose of this paper is to evaluate the performance of a new multiobjective algorithm called Vector Evaluated Population Based Incremental Learning (VEPBIL). The new algorithm was applied in solving a real world application named Reinsurance Contract Optimization (RCO), which is a multiobjective problem consisting of maximizing two conflicting functions: expected return and risk. The VEPBIL was tested on two instances of the problem composed by 7 and 15 layers of real anonymized data. In order to evaluate the algorithm, metrics such as hyper volume, number of solutions and coverage were used. A comparisons against Vector Evaluated Differential evolution (VEDE) is also carried out. The comparison has shown that VEPBIL can dominate about 70% and 50% of solutions from VEDE using 7 and 15 layers respectively, whereas VEDE dominates about 10% and 30% of solutions in the way around.978-1-4673-8418-6/15/$31.00 ©2015 IEEE

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Section: Multiobjective Fundamentalsmentioning

confidence: 99%

A new vector evaluated PBIL algorithm for reinsurance analytics

Cortes

Rau-Chaplin

Prado

2015

2015 Latin America Congress on Computational Intelligence (LA-CCI)

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“…Cortes et al . (2013) considered a multi-layer reinsurance contract consisting of a fixed number of layers. Then, they determined an optimal multi-layer contract such that for a given expected return the associated risk value is minimised.…”

Section: Introductionmentioning

confidence: 99%

An optimal multi-layer reinsurance policy under conditional tail expectation

Najafabadi

Bazaz

2017

Ann. actuar. sci.

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A usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimal criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk, this article generalized an optimal stop-loss reinsurance policy to an optimal multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance policy, this article starts from a given optimal stop-loss reinsurance policy f (·). In the first step, it cuts down an interval [0, ∞) into two intervals [0, M 1 ) and [M 1 , ∞). By shifting the origin of Cartesian coordinate system to (M 1 , f (M 1 )), and showing that under the CT E criteriais, again, an optimal policy. This extension procedure can be repeated to obtain an optimal k-layer reinsurance policy. Finally, unknown parameters of the optimal multi-layer reinsurance policy are estimated using some additional appropriate criteria. Three simulation-based studies have been conducted to demonstrate: (1) The practical applications of our findings and (2) How one may employ other appropriate criteria to estimate unknown parameters of an optimal multi-layer contract. The multi-layer reinsurance policy, similar to the original stop-loss reinsurance policy is optimal, in a same sense. Moreover it has some other optimal criteria which the original policy does not have. Under optimal criterion of minimizing general translative and monotone risk measure ρ(·) of either the insurer's total risk or both the insurer's and the reinsurer's total risks, this article (in its discussion) also extends a given optimal reinsurance contract f (·) to a multi-layer and continuous reinsurance policy.

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“…Recently, the Static Reinsurance Optimization Problem has been the focus of considerable research attention with solutions being proposed based on enumeration [2], single objective evolutionary optimization techniques [3,4], and multi-objective methods [5,6,7]. In the Static Reinsurance Optimization Problem, we start with an almost fully defined reinsurance contract consisting of a fixed number of layers (where each layer has its own limit and deductible and other financial terms) and a simulated set of expected loss distributions (one per layer), plus a model of reinsurance costs and the task is to identifying optimal combinations of placements, i.e., how much of each layer you should buy, such that for a given expected return the associated risk value is minimized.…”

Section: Introductionmentioning

confidence: 99%

Dynamic optimization of multi-layered reinsurance treaties

Wang¹,

Cortes

Rau-Chaplin

2015

Proceedings of the 30th Annual ACM Symposium on Applied Computing

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Risk hedging strategies are at the heart of financial risk management. As with many financial institutions, insurance companies try to hedge their risk against potentially large losses, such as those associated with natural catastrophes. Much of this hedging is facilitated by engaging in risk transfer contracts with the global reinsurance market. Devising an effective hedging strategy depends on careful data analysis and optimization. In this paper, we study from the perspective of an insurance company the Dynamic Reinsurance Optimization problem in which given a set of expected loss distributions (the result of running a Catastrophic Loss Model), a model of reinsurance market costs, and some general financial terms, our task is to evolve a set of complex multi-layered reinsurance contracts that define a Pareto frontier quantifying the best available tradeoffs between expected risk and returns for the insurer. Our approach to this reinsurance contract optimization problem is three fold. Firstly, we apply the Strength Pareto Evolutionary Algorithm 2 (SPEA2) meta-heuristic to guide the multi-objective search process. Secondly, we exploit equation reordering to minimize computation, aggressively pre-computation/caching methods, and discretization to efficiently evaluate individual solutions. Lastly, we apply High Performance Computing (HPC) techniques including shared memory parallelization, vectorization and data prefetching to accelerate the search process. As a result, our prototype Dynamic Reinsurance Optimizer is able to solve industrial sized problems on a single multi-core server in about 2 minutes for 7 layers and 4 minutes for 15 layers per run.

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On PBIL, DE and PSO for Optimization of Reinsurance Contracts

Cited by 9 publications

References 11 publications

A new vector evaluated PBIL algorithm for reinsurance analytics

A new vector evaluated PBIL algorithm for reinsurance analytics

An optimal multi-layer reinsurance policy under conditional tail expectation

Dynamic optimization of multi-layered reinsurance treaties

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