Theoretical Mathematics & Applications

The optimal fuzzy portfolio strategy with option hedging

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• Abstract

  Owing to the fluctuation of financial market from time to time, the risk-free interest rate, volatility and stock price etc may occur imprecisely in the real world. Therefore, it is natural to consider the related parameters fuzzy. Portfolio selection concerns the allocation of wealth to assets such that return is maximized and risk is minimized. The institution hedges the asset's value using put options.This paper proposed the optimal fuzzy hedging portfolio strategy with options, maximizing the expected value of the portfolio and minimizing its Value-at-Risk. One problem with the model for multi-objective portfolio selection is that it is not easy to find a  trade-off between the objectives due to a non-smooth multi-objective optimization problem. We propose a fuzzy programming algorithm to solve the optimization model. As an application, we calculate the optimal invest shares of stocks and put options for an investor seeking for maximum profit and meanwhile reducing risk.