Abstract
This paper studies the portfolio optimization problem with multiple risk measures. More specifically, we use the variance and the Safety First Principle(SFP) as a combined risk measure in mean-risk portfolio optimization model. As the SFP measures the probability that random variable falls below certain level, combining SFP in the mean-variance formulation helps to control the downside risk of the portfolio return. Due to the complexity of such problem, it is difficult to solve such a problem by the traditional stochastic control approach directly. Under some assumptions of the market structure, we transform the incomplete market to complete one and derive the analytical portfolio policy by using the martingale approach. The simulation results exhibit prominent feature of our model in controlling the downside risk of the portfolio model.
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