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

In the presence of reinsurance, an insurer may effectively reduce its (aggregated) loss by partially ceding such a loss to a reinsurer. Stop-loss and quota-share reinsurance contracts are commonly agreed between these two parties. In this paper, we aim to explore a combination of these contracts. The survival functions of the ceded loss and the retained loss are firstly investigated. Optimizing such a reinsurance design is then carried out from the joint perspective of the insurer and the reinsurer. Specifically, we explicitly derive optimal retentions under a criterion of minimizing a convex combination of conditional tail expectations of the insurer’s total loss and the reinsurer’s total loss. In addition, an estimation procedure and more explanations on numerical examples are also presented to find their estimated values.

The Optimal Reinsurance Strategy under Conditional Tail Expectation (CTE) and Wang’s Premium Principle

In this study, we take the conditional tail expectation (CTE) as the constraint condition and consider the optimal reinsurance issues under Wang’s premium principle in general insurance contracts. With the confidence level and the distortion function in Wang’s premium principle given by the insurer in advance, a threshold can be obtained. When the insurer’s risk tolerance level is greater than this value, the optimal reinsurance is a proportional reinsurance in which the deductible equals to this value, else the optimal form of reinsurance is a stop-loss reinsurance. Corresponding numerical examples and economic explanations are also given.

Fair pricing: A framework towards sustainable life insurance products

This research aims to fill the gap in sustainable insurance product study. The central research question of this research is how to develop a fair pricing framework in order to design a sustainable financial product. Current profit testing method is arguably lack of policyholder considerations. The profitability decision under current method only considers profit margin for company. There is no profitability measurement for policyholder. To improve fairness under current pricing, the proposed study proposes a concept of equity in risk between company and policyholder. In order to establish equity in risk, profitability for policyholder needs to be defined and risk measure Conditional Tail Expectation (CTE) for company and policyholder is proposed as a solution. Fairness is achieved if CTE between company and policyholder falls within certain range. CTE generated under new framework could be used as a reference point to all stakeholders to assess the fairness of Unit Linked price. The target population for the study was any regular premium Unit Link product. This research used simple random sampling. From the population consisting of 34 companies 20 samples were drawn. Data is taken from the Indonesian Financial Service Authority. The data used is from the time period between 1 January 2015 and 30 June 2019. Using the CTE, this study finds that most of the Unit Linked pricing are far from fair. It is recommended that companies could be more efficient in their operating and distribution cost in order to be fairer to policyholder and therefore will make the product more sustainable.