Abstract
This paper aims to provide a practical optimal reinsurance scheme under particular conditions, with the goal of minimizing total insurer risk. Excess of loss reinsurance is an essential part of the reinsurance market, but the concept of stop-loss reinsurance tends to be unpopular. We study the purchase arrangement of optimal reinsurance, under which the liability of reinsurers is limited by the excess of loss ratio, in order to generate a reinsurance scheme that is closer to reality. We explore the optimization of limited stop-loss reinsurance under three risk measures: value at risk (VaR), tail value at risk (TVaR), and conditional tail expectation (CTE). We analyze the topic from the following aspects: (1) finding the optimal franchise point with limited stop-loss coverage, (2) finding the optimal limited stop-loss coverage within a certain franchise point, and (3) finding the optimal franchise point with limited stop-loss coverage. We provide several numerical examples. Our results show the existence of optimal values and locations under the various constraint conditions.
Highlights
Reinsurance, an agreement between insurers and reinsurers that allows insurers to transfer and diversify away a certain amount of risk, is the primary risk management tool used by insurance companies
We explore the optimization of limited stoploss reinsurance under three risk measures: value at risk (VaR), tail value at risk (TVaR), and conditional tail expectation (CTE)
Gajek and Zagrodny [3] found that the optimal reinsurance form is the minimum variance under the standard deviation reinsurance principle, and Kaluszka [4] showed that change loss reinsurance is optimal through mean-variance analysis of optimal reinsurance
Summary
Reinsurance, an agreement between insurers and reinsurers that allows insurers to transfer and diversify away a certain amount of risk, is the primary risk management tool used by insurance companies. Mathematical Problems in Engineering reinsurance budget constraints are given, using the principles of minimum CTE and standard deviation reinsurance He notes that, when the reinsurance premium is subject to a small budget, the best form is likely to be limited stoploss reinsurance, not standard stop-loss reinsurance. Li et al [15] modeled the risk process by Brownian motion with drift and studied the optimization problem of maximizing the exponential utility of terminal wealth under the controls of reinsurance and investment. Their results showed that optimal excess of loss reinsurance is generally a better product than optimal proportional reinsurance.
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