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...

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 has considered a risk measure ? and a (maybe incomplete and/or imperfect) arbitrage-free market with pricing rule p. They are said to be compatible if there are no reachable strategies y such that p (y) remains bounded and ?(y) is close to - 8. We show that the lack of compatibility...