• 1 Introduction
  • 2 Acceptance sets
  • 2.1 Financial positions
  • 2.2 Acceptability
  • 3 Required capital and risk measures
  • 3.1 From unacceptable to acceptable
  • 3.2 When is required capital well dened for all nancial positions?
  • 3.3 Risk measures with respect to a single eligible asset
  • 4 Continuity properties of risk measures
  • 4.1 When is required capital a continuous function of nancial positions?
  • 4.2 VaR-acceptability and continuity
  • 4.3 Continuity of convex and coherent risk measures
  • 5 Capital effciency and lack of optimality of the eligible asset
  • 5.1 Equality of risk measures
  • 5.2 Does an optimal eligible asset exist?
  • 6 Appendix