On a subjective approach to risk measurement

This study is based on the analogy between hedging a risky asset and keeping reserves to meet an unknown demand. The optimal hedging level, which depends on individual preferences, is regarded as a measure of risk. We determine the set of optimal levels and investigate the properties of the associated risk measures. This approach provides a new insight into Value at Risk (VaR). We consider it as a solution of a certain optimal inventory problem with linear cost and loss functions. We show that these functions determine the confidence level of VaR. In this way we obtain a simple model that helps us to choose a proper confidence level α and explains why supervisory institutions (such as the Basle Committee) choose a higher α than financial institutions themselves.