We consider the problem of portfolio selection, with transaction costs and constraints on exposure to risk. Linear transaction costs, bounds on the variance of the return, and bounds on different shortfall probabilities are efficiently handled by convex optimization methods. Problems with transaction costs that include a fixed fee, or discount breakpoints, cannot be directly solved by convex op...

This paper deals with a portfolio selection problem based on the possibility theory under the assumption that the returns of assets are LR-type fuzzy numbers. A possibilistic portfolio model with transaction costs is proposed, in which the possibilistic mean value of the return is termed measure of investment return, and the possibilistic variance of the return is termed measure of investment r...

It is widely recognized that when classical optimal strategies are used with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the di¢ culty to estimate expected returns accurately. We propose to parameterize an n stock Black-Scholes model as an n factor Arbitrage Pricing Theory model where eac...

All HARA-utility investors with the same exponent invest in a single risky fund and the risk-free asset. In a continuous time-model stock proportions are proportional to the inverse local relative risk aversion of the investor (1/γ-rule). This paper analyses the conditions under which the optimal buy and hold-portfolio of a HARA-investor can be approximated by the optimal portfolio of an invest...

This paper presents an optimal portfolio selection approach based on value at risk (VaR), conditional value at risk (CVaR), worst-case value at risk (WVaR) and partitioned value at risk (PVaR) measures as well as calculating these risk measures. Mathematical solution methods for solving these optimization problems are inadequate and very complex for a portfolio with high number of assets. For t...

This paper deals with a neural network architecture which establishes a portfolio management system similar to the Black / Litterman approach. This allocation scheme distributes funds across various securities or financial markets while simultaneously complying with specific allocation constraints which meet the requirements of an investor. The portfolio optimization algorithm is modeled by a f...

Robust portfolio optimization aims to maximize the worst-case portfolio return given that the asset returns are allowed to vary 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 mater...

Modern portfolio theory is based on a rational investor choosing the proportions of assets in a portfolio so as to minimize risk and maximize the expected return. In this paper, we investigate the applicability of different stochastic search heuristics to the problem of finding the optimum portfolio. We compare their performance on two problems with known solutions. 1. Portfolio Optimization Gi...

In portfolio optimization, the inverse covariance matrix prescribes the hedge trades where a portfolio of stocks hedges each one with all the other stocks to minimize portfolio risk. In practice with finite samples, however, multicollinearity makes the hedge trades too unstable to be reliable. By reducing the number of stocks in each hedge trade to curb estimation errors, we motivate a “sparse”...

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assum...