The mean-variance formulation by Markowitz in the 1950s paved a foundation for modern portfolio selection analysis in a single period. This paper considers an analytical optimal solution to the mean-variance formulation in multiperiod portfolio selection. Specifically, analytical optimal portfolio policy and analytical expression of the mean-variance efficient frontier are derived in this paper for the multiperiod mean-variance formulation. An efficient algorithm is also proposed for finding an optimal portfolio policy to maximize a utility function of the expected value and the variance of the terminal wealth. Copyright Blackwell Publishers Inc. 2000.

This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be "embedded" into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem.

Exosomes are cell-derived nanovesicles that are involved in the intercellular transportation of materials. Therapeutics, such as small molecules or nucleic acid drugs, can be incorporated into exosomes and then delivered to specific types of cells or tissues to realize targeted drug delivery. Targeted delivery increases the local concentration of therapeutics and minimizes side effects. Here, we present a detailed review of exosomes engineering through genetic and chemical methods for targeted drug delivery. Although still in its infancy, exosome-mediated drug delivery boasts low toxicity, low immunogenicity, and high engineerability, and holds promise for cell-free therapies for a wide range of diseases.

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Targeted delivery to the diseased cell or tissue is the key to the successful clinical use of nucleic acid drugs. In particular, delivery of microRNA-140 (miRNA-140, miR-140) into chondrocytes across the dense, nonvascular extracellular matrix of cartilage remains a major challenge. Here, we report the chondrocyte-targeting exosomes as vehicles for the delivery of miR-140 into chondrocytes as a new treatment for osteoarthritis (OA). By fusing a chondrocyte-affinity peptide (CAP) with the lysosome-associated membrane glycoprotein 2b protein on the surface of exosomes, we acquire CAP-exosomes that can efficiently encapsulate miR-140, specifically enter, and deliver the cargo into chondrocytes in vitro. CAP-exosomes, in contrast to nontagged exosome vesicles, are retained in the joints after intra-articular injection with minimal diffusion in vivo. CAP-exosomes also deliver miR-140 to deep cartilage regions through the dense mesochondrium, inhibit cartilage-degrading proteases, and alleviate OA progression in a rat model, pointing toward a potential organelle-based, cell-free therapy of OA.