The Combined Stop-Loss and Quota-Share Reinsurance: Conditional Tail Expectation-Based Optimization from the Joint Perspective of Insurer and Reinsurer

Syuhada, Khreshna; Hakim, Arief Rachman; Sari, Syandra

doi:10.3390/risks9070125

Cited by 3 publications

(4 citation statements)

References 33 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Selain itu, metode TVaR juga dikenal sebagai Conditional Tail Expectation (CTE), yang lebih umum dalam penggunaannya. Syuhada et al (2021) telah mengilustrasikan penggunaan metode optimisasi berbasis CTE dalam mengevaluasi kombinasi reasuransi stop-loss dan quota-share.…”

Section: Pendahuluanunclassified

Ambang Batas Reasuransi Non-Proporsional Menggunakan Tail Value-At-Risk (TVaR) dari Distribusi Peluang Campuran

Eurico,

Afifatul Ayu Astiani,

I Kadek Darma Arnawa

et al. 2023

JSA

View full text Add to dashboard Cite

One of the tasks of banking institutions is to channel funds to the public through loan products. Banking institutions transfer the risk of non-performing loans to insurance companies and then partially reinsured to reinsurers. The purpose of this study is to determine the non-proportional reinsurance threshold based on the risk of loss of the 20% largest loan principal, using the Tail Value-at-Risk (TVaR) method. The threshold value will be estimated using a sample of 5,000 loans principal. The loan characteristics can be described by a Mixture Gamma Distribution consisting of components with different weights and parameters. The weights and parameters are 19% from the Gamma distribution with parameters α = 2.45 and β = 0.04, 34.5% from Gamma with parameters α = 8.29 and β = 0.07, and 46.5% from Gamma with parameters α = 30 and β = 0.13. Analysis using TVaR produces a threshold value of 274.9 million rupiah. In real cases, if the claim value exceeds 274.9 million rupiah. The insurance company will bear a value of 274.9 million rupiah and the reinsurer will bear the difference in the size of the claim against the threshold limit.

show abstract

Section: Pendahuluanunclassified

Ambang Batas Reasuransi Non-Proporsional Menggunakan Tail Value-At-Risk (TVaR) dari Distribusi Peluang Campuran

Eurico,

Afifatul Ayu Astiani,

I Kadek Darma Arnawa

et al. 2023

JSA

View full text Add to dashboard Cite

show abstract

“…The approach of considering benefits to the insurer and reinsurer in combination is relative rare in the existing literature. Syuhada et al (2021) consider only specific types of contracts: combined stop-loss and quota-share, reinsurance and present conditional tail expectation (CTE)-based optimization from the joint perspective of the insurer and reinsurer. Chen (2021) studied the optimal reinsurance contracts that minimize the convex combination of the conditional value-at-risk (CVaR) of the insurer and reinsurer's losses over the class of ceded loss functions such that the retained loss function is increasing, and the ceded loss function satisfies the Vajda condition.…”

Section: Introductionmentioning

confidence: 99%

“…The approach of considering benefits to the insurer and reinsurer in combination is relative rare in the existing literature. Syuhada et al . (2021) consider only specific types of contracts: combined stop-loss and quota-share, reinsurance and present conditional tail expectation (CTE)-based optimization from the joint perspective of the insurer and reinsurer.…”

Section: Introductionmentioning

confidence: 99%

Pricing reinsurance and determining optimal retention based on the criterion of maximizing social expected utility

Mao

Ostaszewski

2023

EJMBE

View full text Add to dashboard Cite

PurposeThe authors consider the mutual benefits of the ceding company and reinsurance company in the design of reinsurance contracts. Two objective functions to maximize social expected utilities are established, which are to maximize the sum of the expected utilities of both the ceding company and reinsurance company, and to maximize their products. The first objective function, additive, emphasizes the total gains of both parties, while the second, multiplicative, accounts for the degree of substitution of gains of one party through the loss of the other party. The optimal price and retention of reinsurance are found by a grid search method, and numerical analysis is conducted. The results indicate that the optimal solutions for two objective functions are quite different. However, optimal solutions are sensitive to the change of the means and volatilities of the claim loss for both objective functions. The results are potentially valuable to insurance regulators and government entities acting as reinsurers of last resort.Design/methodology/approachIn this paper, the authors apply relatively simple, but in the view significant, methods and models to discuss the optimization of excess loss reinsurance strategy. The authors only consider the influence of loss distribution on optimal retention and reinsurance price but neglect the investment factor. The authors also consider the benefits of both ceding company and reinsurance company to determine optimal premium and retention of reinsurance jointly based on maximizing social utility: the sum (or the product) of expected utilities of reinsurance company and ceding company. The authors solve for optimal solutions numerically, applying simulation.FindingsThis paper establishes two optimization models of excess-of-loss reinsurance contract against catastrophic losses to determine optimal premium and retention. One model considers the sum of the expected utilities of a ceding company and a reinsurance company's expected utility; another considers the product of them. With an example, the authors find the optimal solutions of premium and retention of excess loss reinsurance. Finally, the authors carry out the sensitivity analysis. The results show that increasing the means and the volatilities of claim loss will increase the optimal retention and premium. For objective function I, increasing the coefficients of risk aversion of or reducing the coefficients of risk aversion of will make the optimal retention reduced but the optimal premium increased, and vice versa. However, for objective function 2, the change of coefficient of risk aversion has no effect on optimal solutions.Research limitations/implicationsUtility of the two partners: The ceding company and the reinsurance company, may have different weights and different significance. The authors have not studied their relative significance. The simulation approach in numerical methods limits us to the probability distributions and stochastic processes the authors use, based on, generally speaking, lognormal models of rates of return. This may need to be generalized to other returns, including possible models of shocks through jump processes.Practical implicationsIn the recent two decades, reinsurance companies have played a great role in hedging mega-catastrophic losses. For example, reinsurance companies (and special loss sharing arrangements) paid as much as two-thirds of the insured losses for the September 11, 2001 tragedy. Furthermore, large catastrophic events have increased the role of governments and regulators as reinsurers of last resort. The authors hope that the authors provide guidance for possible balancing of the needs of two counterparties to reinsurance contracts.Social implicationsNearly all governments around the world are engaged in regulation of insurance and reinsurance, and some are reinsurers themselves. The authors provide guidance for them in these activities.Originality/valueThe authors believe this paper to be a completely new and original contribution in the area, by providing models for balancing the utility to the ceding insurance company and the reinsurance company.

show abstract

“…After the work of Cai and Tan (2007), many researchers extended their works in multiple ways by employing various risk measures, various sets of the ceded loss functions, or various premium principles. See, for example, Cai et al (2008), Tan et al (2009), Chi and Tan (2011), Cai et al (2016), Tan et al (2020), Syuhada et al (2021), Sari and Syuhada (2022), and the references therein. Among most of the studies listed above, the insurance premium Y is fixed, and the correlation between the claim amount X and the insurance premium Y in the risk model is neglected.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Optimal Combination of Proportional and Stop-Loss Reinsurance with Dependent Claim and Stochastic Insurance Premium

Sari

Hakim

Magdalena

et al. 2023

JRFM

Self Cite

View full text Add to dashboard Cite

This paper investigates an optimal reinsurance policy using a risk model with dependent claim and insurance premium by assuming that the insurance premium is random. Their dependence structure is modeled using Sarmanov’s bivariate exponential distribution and the Farlie–Gumbel–Morgenstern (FGM) copula-based bivariate exponential distribution. The reinsurance premium paid by the insurer to the reinsurer is fixed and is charged by the expected value premium principle (EVPP) and standard deviation premium principle (SDPP). The main objective of this paper is to determine the proportion and retention limit of the optimal combination of proportional and stop-loss reinsurance for the insurer. Specifically, with a constrained reinsurance premium, we use the minimization of the Value-at-Risk (VaR) of the insurer’s net cost. When determining the optimal proportion and retention limit, we provide some numerical examples to illustrate the theoretical results. We show that the dependence parameter, the probability of claim occurrence, and the confidence level have effects on the optimal VaR of the insurer’s net cost.

show abstract

The Combined Stop-Loss and Quota-Share Reinsurance: Conditional Tail Expectation-Based Optimization from the Joint Perspective of Insurer and Reinsurer

Cited by 3 publications

References 33 publications

Ambang Batas Reasuransi Non-Proporsional Menggunakan Tail Value-At-Risk (TVaR) dari Distribusi Peluang Campuran

Ambang Batas Reasuransi Non-Proporsional Menggunakan Tail Value-At-Risk (TVaR) dari Distribusi Peluang Campuran

Pricing reinsurance and determining optimal retention based on the criterion of maximizing social expected utility

Modeling the Optimal Combination of Proportional and Stop-Loss Reinsurance with Dependent Claim and Stochastic Insurance Premium

Contact Info

Product

Resources

About