Prices of contracts with risky aspects are typically linked to specific uncertainties and probabilities of adverse scenarios. Insurance companies carry the risk of losses in exchange for a premium, which depends on the loss distribution. Another example where risk is exchanged for a fixed price...

This paper formulates a relaxed risk parity optimization model to control the balance of risk parity violation against the total portfolio performance. Risk parity has been criticized as being overly conservative and it is improved by re-introducing the asset expected returns into the model and...