As a contribution to the discussion on the risks of stocks in the long run the present paper analyses the shortfall risks of stocks using the risk measures shortfall probability, mean excess loss and shortfall expectation for various deterministic as well as a stochastic benchmark. As a main...

The present study focuses on the defined financial benefits capital investors have undertaken to pay to their contracting parties during the withdrawal phase under contracts making provision for old age (also referred to as Riester contracts in Germany). The Alterszertifizierungsgesetz requires...

Retirees must draw down their accumulated assets in an orderly fashion, so as not to exhaust their funds too soon. We compare alternative phased withdrawal strategies to a life annuity benchmark using German data; one particular phased withdrawal rule seems attractive, as it offers relatively low...

Retirees must draw down their accumulated assets in an orderly fashion so as not to exhaust their funds too soon. We derive the optimal retirement portfolio from a menu that includes payout annuities as well as an investment allocation and a withdrawal strategy, assuming risk aversion,...

Retirees must draw down their accumulated assets in an orderly fashion so as not to exhaust their funds too soon. We derive the optimal retirement portfolio from a menu that includes payout annuities as well as an investment allocation and a withdrawal strategy, assuming risk aversion,...