MODELING LIQUIDITY EFFECTS IN DISCRETE TIME

We study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox–Ross–Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.     

Robust min–max portfolio strategies for rival forecast and risk scenarios

We consider an extension of the Markowitz mean–variance optimization framework to multiple return and risk scenarios. It is well known that asset return forecasts and risk estimates are inherently inaccurate. The method proposed provides a means for considering rival representations of the future. The optimal portfolio is computed, simultaneously with the worst case, to take account of all rival scenarios. This is a min-max strategy which is essentially equivalent to a robust pooling of the scenarios. Robustness is ensured by the noninferiority of min–max. For example, a basic worst-case optimal return is guaranteed in view of multiple return scenarios. If robustness happens to have too high a cost, guided by the min–max pooling, it is also possible to explore other pooling alternatives. A min–max algorithm is used to solve the problem and illustrate the robust character of min–max with return and risk scenarios. We study the properties of the min–max risk–return frontier and compare with the potentially suboptimal worst-case where the investment strategy and the worst case are computed separately.     

De binnenlandsche geldmarkt en de Nederlandsche Bank in 1907

Ohne Zusammenfassung