MODIFIED VALUE-AT-RISK BASED OPTIMAL REINSURANCE MODELS

• Main Author: Fratama Sari, Suci
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/85650
• Institution: Institut Teknologi Bandung

Having some of their claims to reinsurance companies transferred is one of financial strategies for managing the risks (claims) of insurance companies. With part of the coverage transferred to reinsurance companies, insurance companies incur additional costs in the form of reinsurance premiums that are paid to a reinsurance company. The higher the claims assumed by a reinsurance company, the higher the premium that must be paid. Yet, reinsurance companies can also reduce reinsurance premiums by increasing the expected claims assumed by the insurance company, indicating a balance is required between claims ceded and claims retained, that further leads to an optimal reinsurance model related to the optimal risk (claim) sharing between the insurance company and reinsurance company. This dissertation constructs three optimal reinsurance models with different approaches, with the first model focusing on two important aspects i.e. total cost and proportional reinsurance contract. The total cost here is referred to the total insurance cost measured by Value-at-Risk (VaR) and its modifications, where a proportional reinsurance contract is used as the reinsurance contract in this model. With numerical simulations, an optimal proportion emerged as the result, through which total insurance cost are reduced. Further, an analysis has also been carried out to study the relationship between the optimal proportion and the minimum value of total insurance cost. The second model is an optimal reinsurance model based on total insurance and reinsurance cost, and similar to the first model, its total insurance cost is also measured by VaR and its modifications, with the risk measure applied to total reinsurance cost. A combination of proportional and stop-loss reinsurance contract is used as the reinsurance contract in this model. Numerical simulations were conducted to analyse how proportion and retention are related to the minimum value of total insurance and reinsurance cost. As for the third model, an optimal reinsurance model has been constructed with the net insurance cost in its consideration, where assumption of dependence was involved between the insurance premium and the claim. Assumption of dependence is illustrated by bivariate exponential distribution and FGM copula. In this model, it is assumed that net cost of insurance is measured by VaR, where a combination of proportional and stop-loss reinsurance contracts is used as the reinsurance contract. Numerical simulations were conducted to analyse three aspects: the effect of assumption of dependence between the insurance premium and the claim on the net cost of insurance; the effect of claim occurrence probability on proportion, retention, and net cost of insurance; and to what extent proportion and retention are related to the minimum value of net cost of insurance.