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

Suci Sari, Arief Hakim, Ikha Magdalena and Khreshna Syuhada ()
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Suci Sari: Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
Arief Hakim: Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
Ikha Magdalena: Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
Khreshna Syuhada: Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia

JRFM, 2023, vol. 16, issue 2, 1-20

Abstract: 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.

Keywords: net cost; stochastic insurance premium; copula; value-at-risk (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2023
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