In standard portfolio theory, an investor is typically taken as having one stochastic objective, to maximize the random variable of portfolio return. But in this paper, we focus on investors whose purpose is to build, more broadly, a "suitable portfolio" taking additional concerns into account. Such investors would have additional stochastic and deterministic objectives that might include liquidity, dividends, number of securities in a portfolio, social responsibility, and so forth. To accommodate such investors, we develop a multiple criteria portfolio selection formulation, corroborate its appropriateness by examining the sensitivity of the nondominated frontier to various factors, and observe the conversion of the nondominated frontier to a nondominated surface. Furthermore, multiple criteria enable us to provide an explanation as to why the "market portfolio," so often found deep below the nondominated frontier, is roughly where one would expect it to be with multiple criteria. After commenting on solvability issues, the paper concludes with the idea that what is the "modern portfolio theory" of today might well be interpreted as a projection onto two-space of a real multiple criteria portfolio selection problem from higher dimensional space.
Molecular tools capable of providing information on a target analyte in an organelle of interest are especially appreciated. Traditionally, organelle-targetable probes are designed by incorporating an organelle-specific guiding unit to target the probe molecules into the organelle. The imperfect targeting function of the guiding unit and nonspecific distribution of the analyte in cytosol and each organelle would lead to low spatiotemporal resolution and limited sensitivity. To solve this problem, we report herein a new approach for detection of a target analyte in a specific organelle by engineering a target and location dual-controlled molecular switch. For this proof-of-concept study, fluorescent detection of H2S in lysosomes was performed with a simultaneous H2S and proton-activatable probe based on the acidic environment of lysosomes. The new synthesized fluorescent sensor, "SulpHensor", which contains a spirolactam moiety to bind hydrogen protons and an azide group to react with H2S, displays highly sensitive and selective fluorescence response to H2S under lysosomal pH environment but is out of operation in neutral cytosol and other organelles. Fluorescence imaging shows that SulpHensor is membrane-permeable and suitable for visualization of both the exogenous and endogenous H2S in lysosomes of living cells. The good performance of our proposed approach for H2S sensing demonstrates that this strategy might open up new opportunities for the development of efficient subcellular molecular tools for bioanalytical and biomedical applications.
Computing the nondominated set of a multiple objective mathematical program has long been a topic in multiple criteria decision making. In this paper, motivated by the desire to extend Markowitz portfolio selection to an additional linear criterion (dividends, liquidity, sustainability, etc.), we demonstrate an exact method for computing the nondominated set of a tri-criterion program that is all linear except for the fact that one of its objectives is to minimize a convex quadratic function. With the nondominated set of the resulting quad-lin-lin program being a surface composed of curved platelets, a multiparametric algorithm is devised for computing the platelets so that they can be graphed precisely. In this way, graphs of the tri-criterion nondominated surface can be displayed so that, as in traditional portfolio selection, a most preferred portfolio can be selected while in full view of all other contenders for optimality. Finally, by giving an example for socially responsible investors, we demonstrate that our algorithm can outperform standard portfolio strategies for multicriterial decision makers.
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