Hisashi Yamamoto

Random Matrix Approach for Primal-Dual Portfolio Optimization Problems

In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment concentration under constraints of budget and investment risk (dual problem) for the case that the variances of the return rates of the assets are identical. We analyze both optimization problems by using the Lagrange multiplier method and the random matrix approach. Thereafter, we compare the results obtained from our proposed approach with the results obtained in previous work. Moreover, we use numerical experiments to validate the results obtained from the replica approach and the random matrix approach as methods for analyzing both the primal and dual portfolio optimization problems.

Worker assignment optimization under reset limited-cycled model with multiple periods — Focus on worker's clever tasks

In uncertain cases, the result and efficiency of current period (or production cycle) are influenced not only by the risks which exist in current period but also by the risks which exist in the previous ones. What is more, the risk itself is also affected greatly by the risks which exist in the earlier periods. This kind of problem is called a limited-cycle problem with multiple periods. Normally, workers efficiency is different on different tasks. How can we get an optimal assignment to minimize the total expected costs? In this paper, we consider the optimal worker assignment considering two kinds of efficiency, clever or poor efficiency on tasks. The regularity will be described that n-2 workers have two clever tasks of all, 2 worker has no clever task by contrast. Also, some numerical experiments will be done to check out the regularity of the optimal assignment that each worker has three clever tasks.