The solution for the state price vector is unique because the coefficient matrix of the resulting linear pricing system has a nonzero determinant. A nonzero determinant guarantees that the system of linear equations has exactly one unique solution for the unknown state prices.
Conditions: The market model has three states and three traded assets.; The pricing system is a 3x3 linear system.; The coefficient matrix of the system is nonsingular (determinant is nonzero).
The solution for the state price vector is unique because the coefficient matrix of the resulting linear pricing system has a nonzero determinant. A nonzero determinant guarantees that the system of linear equations has exactly one unique solution for the unknown state prices.
Conditions: The market model has three states and three traded assets.; The pricing system is a 3x3 linear system.; The coefficient matrix of the system is nonsingular (determinant is nonzero).