This paper considers a portfolio selection problem in which portfolios with minimum number of active assets are sought. This problem is motivated by the need of inducing sparsity on the selected portfolio to reduce transaction costs, complexity of portfolio management, and instability of the solution. The resulting problem is a difficult combinatorial problem. We propose … Read more
Portfolio optimisation for a Fund of Hedge Funds (“FoHF”) has to address the asymmetric, non-Gaussian nature of the underlying returns distributions. Furthermore, the objective functions and constraints are not necessarily convex or even smooth. Therefore traditional portfolio optimisation methods such as mean-variance optimisation are not appropriate for such problems and global search optimisation algorithms could … Read more
Portfolio optimization problems involving Value-at-Risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR … Read more
In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution … Read more
The objective of this study is to construct fund-of-funds (FoF) that follow an absolute return strategy and meet the requirements imposed by the Value-at-Risk (VaR) market risk measure. We propose the VaR-Black Litterman model which accounts for the VaR and trading (diversification, buy-in threshold, liquidity, currency) requirements. The model takes the form of a probabilistic … Read more
Recently, several optimization approaches for portfolio selection have been proposed in order to alleviate the estimation error in the optimal portfolio. Among such are the norm-constrained variance minimization and the robust portfolio models. In this paper, we examine the role of the norm constraint in the portfolio optimization from several directions. First, it is shown … Read more
An Asset-Liability Management model with a novel strategy for controlling risk of underfunding is presented in this paper. The basic model involves multiperiod decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities. Therefore it is well-suited to a stochastic programming approach. A stochastic dominance concept is applied to measure … Read more
Robust portfolio optimization finds the worst-case portfolio return given that the asset returns are realized within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns … Read more
This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral … Read more
In many industries, investment is part of the most important planning decisions. In past decades, mathematical programming models have been widely used in capacity planning and facility location to support investment decisions. Such initial techniques evolved to the use of enterprise portfolio management, very common in the energy industry. Increasing concern on risk made of … Read more