Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Operations Research

The pension has an important role in the economy where these reserves are invested in a variety of stocks and bonds on financial markets, such as government bonds, mutual funds and corporate stocks. The thesis focuses on fuzzy interest rate, which represents the main variable to calculate the net present value of liabilities and contributions, and then determine the financial position of the pension funds and determine whether there is surplus or actuarial deficit in the fund through which the decision maker is aware of the financial situation of the fund of the financial position of the fund so as to avoid insolvency risk. In fuzzy environment this thesis modifies Markowitz{u2019}s model by adding new constraint that responsible for secure the pension fund against insolvency risk i.e. ability for cover all participant{u2019}s liabilities along horizon where the return is triangle fuzzy number. This thesis is organized as follows. Chapter (1) presents introduction for the thesis and "Pension funds" includes its plans and types. Chapter (2) introduces basics about fuzzy sets and fuzzy numbers. Chapter (3) presents possibilistic asset allocation optimization model with realistic constraints. Chapter (4) provides a numerical example, conclusions and future research directions, and finally references

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