On robust mean-variance portfolios

We derive closed-form portfolio rules for robust mean–variance portfolio optimization where the return vector is uncertain or the mean return vector is subject to estimation errors, both uncertainties being confined to an ellipsoidal uncertainty set. We consider different mean–variance formulations allowing short sales, and derive closed-form optimal portfolio rules in static and dynamic settings.     

Pivotal methods for computing equilibrium points: Unified approach and new restart algorithm

On the basis of a unified approach to pivotal algorithms and a generalization of the concept of primitive sets by Scarf we show that Scarf's algorithm for finding fixed points can be embedded into a class of more flexible and more efficient algorithms, allowing restarts. An example of this new restart method is described. Also the class of equilibrium problems solvable by this method is discussed.     

Optimal rebalancing of portfolios with transaction costs

Rebalancing of portfolios with a concave utility function is considered. It is proved that transaction costs imply that there is a no-trade region where it is optimal not to trade. For proportional transaction costs, it is optimal to rebalance to the boundary when outside the no-trade region. With flat transaction costs, the rebalance from outside the no-trade region should be to an internal state in the no-trade region but never a full rebalance. The standard optimal portfolio theory is extended to an arbitrary number of equally treated assets, general utility function and more general stochastic processes. Examples are discussed.     

Optimal portfolios with asymptotic criteria

This paper is concerned with a portfolio optimization model for a long planning horizon. We first argue that in this case the asymptotic growth rate and the asymptotic variance are better measures of performance than the usual mean and variance of return. We next propose an efficient algorithm for calculating the asymptotic frontier, i.e., the efficient frontier relative to the new criteria. Finally, we illustrate our methods and compare the difference between our model and the classical mean-variance-model by using historical data based on the 1064 stocks of the Tokyo Stock Exchange.     

Optimal portfolios: new variations of an old theme

We survey some recent developments in the area of continuous-time portfolio optimization. These will include the use of options and of defaultable assets as investment classes and the presentation of a worst-case investment approach that takes the possibility of stock market crashes into account.      

On the convergence of asynchronous parallel algorithm for large-scale linearly constrained minimization problem

As a synchronization parallel framework, the parallel variable transformation (PVT) algorithm is effective to solve unconstrained optimization problems. In this paper, based on the idea that a constrained optimization problem is equivalent to a differentiable unconstrained optimization problem by introducing the Fischer Function, we propose an asynchronous PVT algorithm for solving large-scale linearly constrained convex minimization problems. This new algorithm can terminate when some processor satisfies terminal condition without waiting for other processors. Meanwhile, it can enhances practical efficiency for large-scale optimization problem. Global convergence of the new algorithm is established under suitable assumptions. And in particular, the linear rate of convergence does not depend on the number of processors.     

Convergence properties of Beale-Powell restart algorithm

The Beale-Powell restart algorithm is highly useful for large-scale unconstrained optimization. An example is taken to show that the algorithm may fail to converge. The global convergence of a slightly modified algorithm is proved. Project partially supported by the National Natural Science Foundation of China.     

Continuous-time mean-variance portfolios: a comparison

In this article, we present and compare three mean-variance optimal portfolio approaches in a continuous-time market setting. These methods are the L ²-projection as presented in Schweizer [M. Schweizer, Approximation of random variables by stochastic integrals, Ann. Prob. 22 (1995), pp. 1536–1575], the Lagrangian function approach of Korn and Trautmann [R. Korn and S. Trautmann, Continuous-time portfolio optimization under terminal wealth constraints, ZOR-Math. Methods Oper. Res. 42 (1995), pp. 69–92] and the direct deterministic approach of Lindberg [C. Lindberg, Portfolio optimization when expected stock returns are determined by exposure to risk, Bernoulli 15 (2009), pp. 464–474]. As the underlying model, we choose the recent innovative market parameterization introduced by Lindberg (2009) that has the particular aim to overcome the estimation problems of the stock price drift parameters. We derive some new results for the Lagrangian function approach, in particular explicit representations for the optimal portfolio process. Further, we compare the different optimization frameworks in detail and highlight their attractive and not so attractive features by numerical examples.     

An automatic algorithm selection approach for the multi-mode resource-constrained project scheduling problem

This paper investigates the construction of an automatic algorithm selection tool for the multi-mode resource-constrained project scheduling problem (MRCPSP). The research described relies on the notion of empirical hardness models. These models map problem instance features onto the performance of an algorithm. Using such models, the performance of a set of algorithms can be predicted. Based on these predictions, one can automatically select the algorithm that is expected to perform best given the available computing resources. The idea is to combine different algorithms in a super-algorithm that performs better than any of the components individually. We apply this strategy to the classic problem of project scheduling with multiple execution modes. We show that we can indeed significantly improve on the performance of state-of-the-art algorithms when evaluated on a set of unseen instances. This becomes important when lots of instances have to be solved consecutively. Many state-of-the-art algorithms perform very well on a majority of benchmark instances, while performing worse on a smaller set of instances. The performance of one algorithm can be very different on a set of instances while another algorithm sees no difference in performance at all. Knowing in advance, without using scarce computational resources, which algorithm to run on a certain problem instance, can significantly improve the total overall performance.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASUREgS

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

Static and dynamic VaR constrained portfolios with application to delegated portfolio management

We give a closed-form solution to the single-period portfolio selection problem with a Value-at-Risk (VaR) constraint in the presence of a set of risky assets with multivariate normally distributed returns and the risk-less account, without short sales restrictions. The result allows to obtain a very simple, myopic dynamic portfolio policy in the multiple period version of the problem. We also consider mean-variance portfolios under a probabilistic chance (VaR) constraint and give an explicit solution. We use this solution to calculate explicitly the bonus of a portfolio manager to include a VaR constraint in his/her portfolio optimization, which we refer to as the price of a VaR constraint.     

A fast parallel algorithm for finding Hamiltonian cycles in dense graphs

Suppose that 0<η<1 is given. We call a graph, G, on n vertices an η-Chvátal graph if its degree sequence d₁≤d₂≤?≤d_n satisfies: for k<n/2, d_k≤min{k+ηn,n/2} implies d_n−k−ηn≥n−k. (Thus for η=0 we get the well-known Chvátal graphs.) An -algorithm is presented which accepts as input an η-Chvátal graph and produces a Hamiltonian cycle in G as an output. This is a significant improvement on the previous best -algorithm for the problem, which finds a Hamiltonian cycle only in Dirac graphs (δ(G)≥n/2 where δ(G) is the minimum degree in G).     

On the convergence property of the DFP algorithm

The DFP algorithm of unconstrained optimization possesses excellent properties of convergence for convex functions. However, a convergence theory of the DFP algorithm without the convexity assumption has not yet been established. This paper gives the following result: If the objective function is suitably smooth, and if the DFP algorithm produces a convergent point sequence, then the limit point of the sequence is a critical point of the objective function. Also, some open questions are mentioned.Supported by the National Science Foundation of China.     

Degree constrained book embeddings

A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine), and an assignment of edges to half-planes with the spine as boundary (the pages), so that edges assigned to the same page can be drawn on that page without crossings. Given a graph G=(V,E), let be a function such that 1f(v)deg(v). We present a Las Vegas algorithm which produces a book embedding of G with pages, such that at most f(v) edges incident to a vertex v are on a single page. This result generalises that of Malitz [J. Algorithms 17 (1) (1994) 71–84].     

Comparison of optimal portfolios with and without subsistence consumption constraints

We present the effects of the subsistence consumption constraints on a portfolio selection problem for an agent who is free to choose when to retire with a constant relative risk aversion (CRRA) utility function. By comparing the previous studies with and without the constraints expressed by the minimum consumption requirement, the changes of a retirement wealth level and the amount of money invested in the risky asset are derived explicitly. As a result, the subsistence constraints always lead to lower retirement wealth level but do not always induce less investment in the risky asset. This implies that even though the agent who has a restriction on consumption retires with lower wealth level, she invests more money near the retirement when her risk aversion lies inside a certain range.     

Admissible investment strategies in continuous trading

We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we show that any such plan has a certain optimality property known to hold also in discrete time models. Moreover, we show that this optimality criterion can be simplified significantly. In particular we show how admissibility can be related directly to observable characteristics of the investment strategy.     

Portfolio Optimization Model with Transaction Costs

Abstract The purpose of the article is to formulate,under the l_∞ risk measure,a model of portfolio selectionwith transaction costs and then investigate the optimal strategy within the proposed.The characterization of aoptimal strategy and the efficient algorithm for finding the optimal strategy are given.     

Parallel SSLE algorithm for large scale constrained optimization

In this paper, a parallel SSLE algorithm is proposed for solving large scale constrained optimization with block-separable structure. At each iteration, the PVD sub-problems are solved inexactly by the SSLE algorithm, which successfully overcomes the constraint inconsistency exited in most SQP-type algorithm, and decreases the computation amount as well. Without assuming the convexity of the constraints, the algorithm is proved to be globally convergent to a KKT point of the original problem.     

A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.