In this contribution we propose a dynamic tracking error problem and we consider the problem of monitoring at discrete point the shortfall of the portfolio below a set of given reference levels of wealth. We formulate and solve the resulting dynamic optimization problem using stochastic...

A fast method based on coordinate-wise descent algorithms is developed to solve portfolio optimization problems in which asset weights are constrained by Lq norms for 1=q=2. The method is first applied to solve a minimum variance portfolio (mvp) optimization problem in which asset weights are...

In this paper we propose a quasi-shrinkage approach for minimum-variance portfolios which does not use a quadratic loss function to derive the optimal shrinkage intensity. We develop two alternative objective functions for linear shrinkage. The first targets the reduction of portfolio variance....

Proceeding to portfolio allocation in the framework of Markowitz, a numerical inconsistency may occur when the sample covariance matrix of assets returns has to be inverted. This is mainly caused by the magnitude of its lowest eigenvalues. In this paper, we tackle the Markowitz problem as an...

In this paper we introduce a simple, yet flexible approach to construct (enhanced) index tracking portfolios. PADME (Portfolio Allocation via Density MatchEs) uses the density function of returns as a robust means of capturing investor preferences, and identifies suitable portfolios through a...

We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called probability of drawdown, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its maximum value to date. We assume that the portfolio is...

We study the boundedness properties of the value function for a general worst-case scenario stochastic dynamic programming problem. For the portfolio selection problem,we present sufficient economically reasonable conditions for the finitness and uniform boundedness of the value function. The...

We define a regularized variant of the Dual Dynamic Programming algorithm called REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called...