Reinsurance is a way of transferring some of the risk from the insurer to another party, called the reinsurer, in exchange for a premium. Reinsurance can reduce the insurer’s exposure to large losses, improve its solvency and capital position, and increase its risk-adjusted profitability.
However, reinsurance also has a cost, which can reduce the insurer’s profit margin. Therefore, the insurer needs to decide how much and what type of reinsurance to buy, considering its risk appetite, capital requirements, and business objectives. This is where the reinsurance efficient frontier comes in. Reinsurance efficient frontier is a concept that helps insurers to find the optimal balance between risk and return when buying reinsurance protection.
The reinsurance efficient frontier is a graphical representation of the trade-off between risk and return for different reinsurance structures. A reinsurance structure is a combination of parameters that define the reinsurance contract, such as the retention level, the limit level, the premium rate, and the commission rate. The risk and return of a reinsurance structure can be measured by various indicators, such as the probability of ruin, the expected profit, the risk-adjusted return on equity, or the value-at-risk.
The reinsurance efficient frontier shows the set of reinsurance structures that offer the highest return for a given level of risk, or the lowest risk for a given level of return. These structures are called efficient, because they cannot be improved by changing the reinsurance parameters. Any structure that lies below the efficient frontier is sub-optimal, because it either has lower return for the same risk, or higher risk for the same return.
One way of finding the reinsurance efficient frontier is to use a simulation-based approach, such as Dynamic Financial Analysis (DFA). DFA is a method that models the main financial factors affecting the insurer’s performance, such as premiums, losses, expenses, reinsurance cost and recoveries, and investment income. By running thousands of simulations, DFA can estimate the distribution of the insurer’s profit and loss, its balance sheet, and solvency under different reinsurance structures. Then, by applying the chosen risk and return measures, DFA can identify the efficient structures and plot them on the reinsurance efficient frontier.
An example of using DFA to find the reinsurance efficient frontier is given in the article “Optimal joint survival reinsurance: An efficient frontier approach” by Dimitrova and Kaishev. The authors considered the problem of optimal excess of loss reinsurance with a limiting and a retention level, and used the probability of joint survival of the insurer and the reinsurer, and the expected profit given joint survival, as the risk and return measures. They show how to derive explicit expressions for these measures, and how to use an efficient frontier type approach to set the optimal reinsurance parameters. They also illustrate their method with numerical examples, using different distributions for the claim amounts. The main conclusions from the article by Dimitrova and Kaishev are as follows: (i) The problem of optimal excess of loss reinsurance with a limiting and a retention level can be solved by combining specific risk and performance measures, under some relatively general assumptions for the risk model; (ii) The probability of joint survival of the insurer and the reinsurer up to a finite time horizon is a suitable risk measure, and the expected profit given joint survival is a suitable performance measure, for this problem; (iii) An efficient frontier type approach can be used to set the optimal reinsurance parameters, based on these measures, and to compare different reinsurance structures; (iv) Explicit expressions for the probability of joint survival and the expected profit given joint survival can be derived for any continuous joint distribution of the claim amounts, and for any non-negative, non-decreasing function of the premium income; and (v) Numerical examples show that the optimal reinsurance parameters depend on the distribution of the claim amounts, and that the dependence is stronger for the case of dependent claim severities than for the case of independent claim severities.
The reinsurance efficient frontier is a powerful tool that can help insurers to optimize their reinsurance decisions and achieve their desired risk-return trade-off. However, it is important to note that the reinsurance efficient frontier is not static, but dynamic, and depends on the changing market conditions, regulatory environment, and customer preferences. Therefore, insurers should constantly monitor and update their reinsurance efficient frontier, and be ready to adapt their reinsurance strategy accordingly.