Optimal Portfolios using Linear Programming Models

The classical Quadratic Programming formulation of the well known portfolio selection problem, is cumbersome, time consuming and relies on two important assumptions: (a) the expected return is multivariate normally distributed; (b) the investor is risk averter. This paper formulates two alternative models, (i) maximin, and (ii) minimization of absolute deviation. Data from a very simple … Read more

Constrained Nonlinear Programming for Volatility Estimation with GARCH Models

The paper proposes a constrained Nonlinear Programming methodology for volatility estimation with GARCH models. These models are usually developed and solved as unconstrained optimization problems whereas they actually fit into nonlinear, nonconvex problems. Computational results on FTSE 100 and S & P 500 indices with up to 1500 data points are given and contrasted to … Read more

Minimum Risk Arbitrage with Risky Financial Contracts

For a set of financial securities specified by their expected returns and variance/covariances we propose the concept of minimum risk arbitrage, characterize conditions under which such opportunities may exist. We use conic duality and convex analysis to derive these characterizations. For practical computation a decidability result on the existence of an arbitrage opportunity is derived. … Read more