This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial...

An arbitrage portfolio provides a cash flow that can never be negative at zero cost. We define the weaker concept of a “desirable portfolio” delivering cash flows with negative risk at zero cost. Although these are not completely risk-free investments and subject to the risk measure used,...

General risk functions are becoming very important in finance and insurance. Many risk functions are interpreted as initial capital requirements that a manager must add and invest in a risk-free security in order to protect his clients wealth. Nevertheless, until now it has not been proved that...

This paper studies a portfolio choice problem such that the pricing rule may incorporate transaction costs and the risk measure is coherent and expectation bounded. We will prove the necessity of dealing with pricing rules such that there are essentially bounded stochastic discount factors,...

The optimal reinsurance problem is a classic topic in Actuarial Mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the...