A kind of optimal investment problem under inflation and uncertain time horizon Abstract   In this paper, we study a kind of optimal investment problem under inflation and uncertain time horizon. It can be generally formulated into a stochastic optimal control problem. In particular for the constant relative risk aversion utility, we employ the method of completion of squares to give an explicit form of optimal portfolio and maximum utility by the solution of a stochastic Riccati equation, whose wellposedness is obtained and also of significance in its own right. The most distinguishing result of our work is that the randomness of exit time actually affects not only the optimal portfolio but also the maximum utility in the case of stochastic market parameters. Moreover, we present several numerical examples to show the application of theoretical results and further discuss the influence of inflation and random time horizon from the economic viewpoint.

Global minimum variance portfolios under uncertainty: a robust optimization approach This paper presents new models which seek to optimize the first and second moments of asset returns without estimating expected returns. Motivated by the stability of optimal solutions computed by optimizing only the second moment and applying the robust optimization methodology which allows to incorporate the uncertainty in the optimization model itself, we extend and combine existing methodologies in order to define a method for computing relativerobust and absoluterobust minimum variance portfolios. For the relative robust strategy, where the maximum regret is minimized, regret is defined as the increase in the investment risk resulting from investing in a given portfolio instead of choosing the optimal portfolio of the realized scenario. The absolute robust strategy which minimizes the maximum risk was applied assuming the worstcase scenario over the whole uncertainty set. Across alternate time windows, results provide new evidence that the proposed robust minimum variance portfolios outperform nonrobust portfolios. Whether portfolio measurement is based on return, risk, regret or modified Sharpe ratio, results suggest that the robust methodologies are able to optimize the first and second moments without the need to estimate expected returns.