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We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. A practical scheme for the long-only fully-invested problem is developed and tested for the classic QP application. The advantage of Monte Carlo methods is that they may be extended to risk functions that are more complicated functions of the return distribution, and that the underlying return distribution may be computed without the classical Gaussian limitations. The optimization of quadratic risk-return functions, VaR, CVaR, may be handled in a similar manner to variability ratios such as Sortino and Omega, or mathematical constructions such as expected utility and its behavioural finance extensions. Robustification is also possible. Grid computing technology is an excellent platform for the development of such computations due to the intrinsically parallel nature of the computation, coupled to the requirement to transmit only small packets of data over the grid. We give some examples deploying GridMathematica, in which various investor risk preferences are optimized with differing multivariate distributions. Good comparisons with established results in Mean-Variance and CVaR optimization are obtained when ``edge-vertex-biased sampling methods are employed to create random portfolios. We also give an application to Omega optimization.
This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance cri
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is necessary to
We present an online approach to portfolio selection. The motivation is within the context of algorithmic trading, which demands fast and recursive updates of portfolio allocations, as new data arrives. In particular, we look at two online algorithms
We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed between choices
In this paper, we propose a market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution is able to