The success of quantitative approaches to portfolio choice crucially depends on the considered return model. Experts however do not agree on which return model is most appropriate. This controversy about the model specification introduces uncertainty in the optimal portfolio choice. We will not meddle in the discussion on which model specification is most appropriate. Instead we consider the ad...

A connection between the notion of information and the concept of risk and return in portfolio theory is deduced. This succeeds in two steps: A general moment-return relation for arbitrary assets is derived, thereafter the total expected return is connected to the Kullback-Leibler information. With this result the optimization problem to maximize the expected return of a portfolio consisting of...

in this paper, the portfolio selection problem is considered, where fuzziness and randomness appear simultaneously in optimization process. since return and dividend play an important role in such problems, a new model is developed in a mixed environment by incorporating fuzzy random variable as multi-objective nonlinear model. then a novel interactive approach is proposed to determine the pref...

Mean-variance criterion has long been the main stream approach in the optimal portfolio theory. The investors try to make a balance between the risk and return on their portfolio. In this paper, the deviation of the asset return from the investor’s expectation in the worst scenario is taken as the measure of risk for portfolio selection. One important advantage of this approach is that the inve...

The growth-optimal portfolio optimization strategy pioneered by Kelly is based on constant portfolio rebalancing which makes it sensitive to transaction fees. We examine the effect of fees on an example of a risky asset with a binary return distribution and show that the fees may give rise to an optimal period of portfolio rebalancing. The optimal period is found analytically in the case of log...

This paper presents two meta-heuristic algorithms to solve an extended portfolio selection model. The extended model is based on the Markowitz's Model, aiming to minimize investment risk in a specified level of return. In order to get the Markowitz model close to the real conditions, different constraints were embedded on the model which resulted in a discrete and non-convex solution space. ...

This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient à la Markowitz. It is shown that, when the market coefficients are deterministic functions of time, a mean-variance efficient portfolio reali...

In this paper we consider the robust portfolio selection problem involving two types of uncertainties; the uncertainty in the distribution of exit time and the uncertainty in the distribution of portfolio return conditional on exit time. To deal with these uncertainties, we propose a tractable approach by applying worst-case VaR strategy to the case where partial information on the exit time di...

In the estimation of portfolios, it is natural to assume that the utility function depends on exogenous variable. From this point of view, in this paper, we develop the estimation under the utility function depending on exogenous variable. To estimate the optimal portfolio, we introduce a function of moments of the return process and cumulant between the return processes and exogenous variable,...