TITLE:
Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition
AUTHORS:
Fengzhu Chang, Ying Fang
KEYWORDS:
Pareto-Optimal Reinsurance, TVaR Risk Measure, Vajda Condition, TVaR Premium Principle
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.13 No.10,
October
18,
2023
ABSTRACT: Reinsurance is an effective risk management tool for insurers to
stabilize their profitability. In a typical reinsurance treaty, an insurer
cedes part of the loss to a reinsurer. As the insurer faces an increasing
number of total losses in the insurance market, the insurer might expect the
reinsurer to bear an increasing proportion of the total loss, that is the
insurer might expect the reinsurer to pay an increasing proportion of the total
claim amount when he faces an increasing number of total claims in the
insurance market. Motivated by this, we study the optimal reinsurance problem
under the Vajda condition. To prevent moral hazard and reflect the spirit of
reinsurance, we assume that the retained loss function is increasing and the
ceded loss function satisfies the Vajda condition. We derive the explicit
expression of the optimal reinsurance under the TVaR risk measure and TVaR
premium principle from the perspective of both an insurer and a reinsurer. Our
results show that the explicit expression of the optimal reinsurance is in the
form of two or three interconnected line segments. Under an additional mild
constraint, we get the optimal parameters and find the optimal reinsurance
strategy is full reinsurance, no reinsurance, stop loss reinsurance, or
quota-share reinsurance. Finally, we gave an example to analyze the impact of
the weighting factor on optimal reinsurance.