Kreps Investment Equivalent Reinsurance Pricing

Kreps’ investment-equivalent approach provides a theoretically sound framework for pricing reinsurance contracts. It moves beyond traditional actuarial methods based primarily on expected losses and adds a crucial layer of risk aversion and market consistency. The core idea is to determine the cost of the reinsurance contract such that the reinsurer is indifferent between accepting the contract and investing its capital in a financial market with comparable risk and return characteristics.

The method begins by modelling the reinsurer’s capital as an investment portfolio. The primary driver of reinsurance pricing then becomes the required return on this capital. This return needs to compensate the reinsurer for bearing the risk associated with the reinsurance contract. A key element is specifying a utility function that reflects the reinsurer’s risk aversion. This function captures how the reinsurer values incremental gains and losses, with a higher degree of risk aversion implying a steeper penalty for potential losses.

The process typically involves simulating the possible outcomes of the reinsurance contract, considering the frequency and severity of claims. These simulations are then used to determine the impact of the contract on the reinsurer’s capital position in various scenarios. For each possible outcome, the utility function is applied to calculate the reinsurer’s satisfaction (or dissatisfaction) with the resulting capital level. These utility values are then averaged, giving an expected utility for holding the reinsurance contract.

The reinsurance premium is then adjusted iteratively until the reinsurer’s expected utility with the contract is equal to the expected utility without the contract. This is the core of the ‘indifference’ principle. It ensures the reinsurer is earning a return on its capital that is equivalent to what it could earn by investing that capital elsewhere in the market with comparable risk.

One of the major advantages of the Kreps framework is its ability to incorporate diverse risk factors. Reinsurers are inherently concerned with not just the expected value of claims, but also with potential extreme events. The utility function allows the reinsurer to explicitly express their aversion to such events, resulting in premiums that adequately reflect the downside risk.

Furthermore, this approach facilitates consistency with capital market pricing. By anchoring the reinsurance pricing to the return requirements on capital in other sectors, it helps to avoid potential arbitrage opportunities. This makes the reinsurance market more efficient and better integrated with the broader financial system.

While theoretically robust, the Kreps investment-equivalent approach presents challenges in practical implementation. Selecting an appropriate utility function that accurately reflects the reinsurer’s preferences can be complex. Moreover, the method often requires extensive simulations and significant computational resources. Despite these challenges, it offers a powerful tool for reinsurers seeking to price contracts in a way that is both risk-aware and market-consistent.