Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 6 2 2015 11 01 Continuous time portfolio optimization 103 112 258 10.22075/ijnaa.2015.258 EN Alireza Bahiraei Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran Behzad Abbasi Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran. Farahnaz Omidi Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran. Nor Aishah Hamzah Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia Abdul Hadi Yaakub Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia Journal Article 2014 11 13 This paper presents dynamic portfolio model based on the Merton's optimal investment-consumption model, which combines dynamic synthetic put option using risk-free and risky assets. This paper is extended version of methodological paper published by Yuan Yao (2012). Because of the long history of the development of foreign financial market, with a variety of financial derivatives, the study on theory or empirical analysis of portfolio insurance focused on how best can portfolio strategies be used in minimizing risk and market volatility. In this paper, stock and risk-free assets are used to replicate options and to establish a new dynamic model to analyze the implementation of the dynamic  process of investors' actions using dynamic replication strategy. Our results show that investors' optimal strategies of portfolio are not dependent on their wealth, but are dependent on market risk and  this new methodology is broaden in compare to paper of Yuan Yao (2012). https://ijnaa.semnan.ac.ir/article_258_df756db274fd1281ef179f49e16f96e4.pdf