Now showing 1 - 2 of 2
  • Publication
    Optimal Design of the Attribution of Pension Fund Performance to Employees
    (Wiley-Blackwell, 2013-06) ;
    The article analyzes risk sharing in a defined contribution pension fund in continuous time. According to a prespecified attribution scheme, the interest rate paid on the employees' accounts is a linear function of the fund's investment performance. For each attribution scheme, the pension fund maximizes the expected utility and the employees derive utility from their savings accounts. It turns out that all Pareto-optimal attribution schemes are characterized by the same optimal participation rate. We derive the total welfare gain that installs from replacing no participation with optimal participation. This welfare gain can be quantified and is substantial for reasonable parameter values.
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    Scopus© Citations 1
  • Publication
    Consumption and Portfolio Optimisation at the End of the Life-Cycle
    (Difo-Druck GmbH, 2007)
    The thesis' focus is on the consumption/portfolio optimisation and the optimal annuitisation decision of a pensioner in a continuous time setting. Technically, this involves solving a combined optimal stopping and optimal control problem (COSOCP). The retiree faces the crucial question of how much to consume and how much to invest in the risky asset (financial market risk). This creates the optimal control aspect of the COSOCP. Any prior decisions on annuities and life insurance are taken as given. The second source of uncertainty is the pensioner's longevity risk, which is why we include an annuity market. The pensioner has to find the optimal time to annuitise his wealth. This constitutes the optimal stopping aspect of the COSOCP. Stabile (2006) provides an appropriate model to solve the mentioned COSOCP. Among other things we mainly contribute a new solution method for this COSOCP via duality arguments, the study of the economically interesting range of relative risk aversions greater than one and the essential inclusion of a bequest motive (annuitisation is in conflict with a potential bequest motive). The first part of the thesis lays down the necessary theoretical foundations for the COSOCP. We model the utility, which the pensioner derives from a stream of consumption or an annuity, and define his utility from bequests. Later, we will specify the pensioner's preferences to power utility and subsistence level utility functions. Afterwards, we discuss the three major ingredients for solving the pensioner's COSOCP: Optimal control theory, optimal stopping theory and mortality concepts. The second part of the thesis exploits the theoretical foundations of the first part. We only solve a pure optimal control problem under the Gompertz-Makeham mortality law. We are able to derive interesting comparisons; however, this problem is already quite involved and helps us to understand why we have to employ the less complicated exponential mortality law in a real COSOCP. The exponential mortality law has the great advantage of increased mathematical tractability. We use it to solve two different models. In the first model we impose that the relative risk aversion is the same for all utility functions: Utility from consumption, annuity and bequests. Most often the annuitisation decision is then of the now-or-never type: Depending on the model parameters, annuitisation either occurs immediately or never (reduction to a pure optimal control problem). We solve both cases and show how the annuitisation decision is influenced by the model parameters. Finally, the second model provides an extension to the first one by allowing for a higher relative risk aversion in the post-annuitisation phase. This last model leads to a real COSOCP in most cases. After exploiting some duality arguments, we arrive at a slightly nonlinear ordinary differential equation for the dual value function. While the no-bequest case allows a quasi-analytical solution, the bequest case has to be solved numerically. We give general characteristics of the optimal consumption and investment rule and numerically show how they depend on the parameters. Finally, we simulate the optimal annuitisation rule.