The optimal portfolios based on a modified safety-first rule with risk-free saving

Yuanyao Ding; Zudi Lu

doi:10.3934/jimo.2016.12.83

Article Contents

2016, Volume 12, Issue 1: 83-102. Doi: 10.3934/jimo.2016.12.83

This issue Previous Article A global optimization approach to fractional optimal control Next Article A full-modified-Newton step infeasible interior-point algorithm for linear optimization

The optimal portfolios based on a modified safety-first rule with risk-free saving

Yuanyao Ding^1, and
Zudi Lu^2,

1.
College of Science & Technology, and Faculty of Business, Ningbo University, Ningbo 315211
2.
Southampton Statistical Sciences Research Institute, and School of Mathematical Sciences, University of Southampton, SO17 1BJ

Received: June 30, 2013

Revised: October 31, 2014

Published: December 2015

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Abstract

How to manage the social security trust funds is a topic of wide interests both academically and professionally. In the setting of portfolio selection with social security funds investment, we propose a modified safety-first (MSF) rule with portfolio selection including risk-free saving. We first demonstrate under some mild assumptions that the solution to the MSF model for an individual investor can be expressed by explicitly analytical formula and the necessary and sufficient conditions for their existence are obtained. We then derive the safety-first efficient frontiers in both the space of expected return and insured return level and the space of standard deviation and expected return, with numerical examples illustrated. By comparing the results of the MSF model with those of the mean-variance (M-V) model, some novel insights into the differences between them are further gained.

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Mathematics Subject Classification: Primary: 91B28; Secondary: 91G10.

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