Capital Asset Pricing Model (CAPM) with drawdown measure

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM) stated in both single and multiple sample-path settings. The drawdown beta in the CAPM has a simple interpretation and is evaluated for hedge fund indices from the HFRX database in the single sample-path setting. Drawdown alpha is introduced similarly to the alpha in the classical CAPM and is evaluated for the same hedge fund indices. Both drawdown beta and drawdown alpha are used to prioritize hedge fund strategies and to identify instruments for hedging against market drawdowns.     

Fuzzy Markov Chains and Decision-Making

Decision-making in an environment of uncertainty and imprecision for real-world problems is a complex task. In this paper it is introduced general finite state fuzzy Markov chains that have a finite convergence to a stationary (may be periodic) solution. The Cesaro average and the -potential for fuzzy Markov chains are defined, then it is shown that the relationship between them corresponds to the Blackwell formula in the classical theory of Markov decision processes. Furthermore, it is pointed out that recurrency does not necessarily imply ergodicity. However, if a fuzzy Markov chain is ergodic, then the rows of its ergodic projection equal the greatest eigen fuzzy set of the transition matrix. Then, the fuzzy Markov chain is shown to be a robust system with respect to small perturbations of the transition matrix, which is not the case for the classical probabilistic Markov chains. Fuzzy Markov decision processes are finally introduced and discussed.     

New distance measures for classifying X-ray astronomy data into stellar classes

Advances in Data Analysis and Classification - The classification of the X-ray sources into classes (such as extragalactic sources, background stars,...) is an essential task in astronomy....     

A note on fundamental,non-fundamental,and robust cycle bases

In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirchhoff) bases, i.e., those that can be derived from a spanning tree, are not necessarily cyclically robust. Here we note that, conversely, cyclically robust bases (even of planar graphs) are not necessarily fundamental. Furthermore, we present a class of cubic graphs for which cyclically robust bases can be explicitly constructed.     

A survey on discriminatory processor sharing

The Discriminatory Processor Sharing (DPS) model is a multi-class generalization of the egalitarian Processor Sharing model. In the DPS model all jobs present in the system are served simultaneously at rates controlled by a vector of weights {g_k > 0; k = 1,..., K }. If there are N_k jobs of class k present in the system, k = 1,..., K, each class-k job is served at rate . The present article provides an overview of the analytical results for the DPS model. In particular, we focus on response times and numbers of jobs in the system. This work is part of a French-Dutch Van Gogh research project funded by NWO (The Netherlands Organization for Scientific Research) and EGIDE under grant VGP 61-520. We also acknowledge the support of EuroNGI Network of Excellence. This work was done while U. Ayesta was an ERCIM Postdoc fellow at CWI.     

Resolvent Expansions on Hybrid Manifolds

We study Laplace-type operators on hybrid manifolds, i.e., on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace–Beltrami operators on each component with some boundary conditions at the points of gluing. The large spectral parameter expansion of the trace of the second power of the resolvent is obtained. Some questions of the inverse spectral theory are addressed.     

The Feichtinger Conjecture for Reproducing Kernels in Model Subspaces

We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace K _Θ=H ²⊖ΘH ² of the Hardy space H ², where Θ is an inner function. First, we verify the Feichtinger conjecture for the kernels [(k)\tilde]_ln=k_ln/||k_ln||\tilde{k}_{\lambda_{n}}=k_{\lambda_{n}}/\|k_{\lambda _{n}}\| under the assumption that sup  _n |Θ(λ _n )|<1. Second, we prove the Feichtinger conjecture in the case where Θ is a one-component inner function, meaning that the set {z:|Θ(z)|<ε} is connected for some ε∈(0,1).     

Zero-sum constrained stochastic games with independent state processes

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints     

Graph Approach to the Computation of the Homology of Continuous Maps

We introduce an efficient algorithm to compute the homomorphism induced in (relative) homology by a continous map. The algorithm is based on a cubical approximation of the map and the theory of multivalued maps. A software implementation of the algorithms introduced in this paper is available at [27].