# Session 20: Practical Math

17.05.2019  |  Time: 10:00-13:00  |  NUUz, Tashkent  |  Conference Room 321, Block C

Analytic solution to the portfolio optimization problem in a mean-variance-skewness model – Prof. Zinovy Landsman

Abstract

In portfolio theory, it is well-known that the distributions of stock returns are often unimodal, asymmetric distributions. Therefore, many researches have suggested considering the skew-normal distribution as an adequate model in quantitative finance. Such asymmetry explains why the celebrated mean-variance theory, which does not account to the skewness of distribution of returns, frequently fails to provide an optimal portfolio selection rule.  In this paper, we provide a novel approach for solving the problem of optimal portfolio selection for asymmetric distributions of the stock returns, by putting it into a framework of a mean-variance-skewness measure. Moreover, our optimal solutions are explicit and are closed-form. In particular, we provide an analytical portfolio optimization solution to the exponential utility of the well-known skew-normal distribution. Our analytical solution can be investigated in comparison to other portfolio selection rules, such as the standard mean-variance model. The new methodology is illustrated numerically.

Scope and Horizons of Industrial Mathematics – Prof. Adir Pridor

Abstract

A short history of industrial mathematics is described and a characterization of industrial mathematics will be proposed followed by outlining the main features and typical work stages of industrial mathematics projects. A somewhat detailed illustration is presented of a project on page outline, related to the printing industry. Academic programs on industrial mathematics will be briefly discussed.

Enhancing Production in Semi-Conductor Plants – Prof. Adir Pridor

Abstract

The efficient operation of a multi-product production line is a very complex combinatorial problem and plants in this family, mainly FABs of the semi-conductor industry, are very much concerned about finding good heuristics for it. The economic outcome of an efficient operation is huge. A comprihensive approach to the problem, based on a simulation-optimization combination, will be presented while illustrating how all relevant operational issues are adequately represented in the model. The proposed model allows the plant owner to apply preferences and policies. Some open problems will be presented.

A Ruler-Of-Justice Policy for Utility-Carrying Queues with Impatience – Prof. Israel David

Abstract

Motivated by the utility-equity dilemma in assigning live organs to patients on the national waiting list, we develop a fair allocation policy among "men" and "jobs", and claim that this policy, and not FCFS, should be used as the yardstick for fairness, although it is not socially optimal in terms of gain.
We simplify the problem by assuming that all individuals are characterized by a general single trait, and that all "men" have a common limit on waiting time.
We then claim that the individually optimal policy is defined by some critical time for each man, for insisting on a match, and implement continuous time optimal-stopping methods and analysis to determine these times.
We evaluate the long-time average gain, the chances to get a match, and the expected waiting time attained by our policy, and then compare them with those attained by FCFS, and a policy which assigns a match only. The results indicate that oftentimes our policy provides higher average gains and better chances to get a match, but also longer waiting times.