A nonlinear programming problem in the space of two scalar parameters is applied to approximate the problem of optimization of a fixed-income portfolio by the quantile quality criterion. Since such securities have limited maturity time, portfolio is formed through reinvestment of the avails obtained upon maturity of securities. A quantile criterion is applied to determine the investment risk due to the uncertainty in future reinvestment. The geometry of the set of admissible values of parameters is studied and an explicit algebraic expression is derived for the optimum of the aim function in the nonlinear programming problem.
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