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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

2 2001

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Necessary and Sufficient Conditions for the Stability of Interval Matrices

Białas S., Jakubowska M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2001

vol. 49, nr 3

467-477

In this paper new necessary and sufficient conditions for the stability of the interval matrix [formula] are presented. These conditions represent a modification of paper [13]. Also, an algorithm for checking the stability of the interval matrix [formula] is proposed. The comparison of efficiency of the new algorithm and the algorithm from paper [13] is demostrated by means of examples.

Extension of Khang's Immunization Formula

Zaremba L.S., Rządkowski G.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2001

vol. 49, nr 3

527-536

The paper presents two theorems on immunization in the continuous context when a liability consists of a single outflow at a known future date. It is assumed in Theorem 1 that interest rates h(O, t) shift to their new values h * (O, t) = h(O, t) + f()..)a(t) where ).. is a random parameter "chosen" by a financial market under consideration, while a(t) is a continuous function and f()..) is twice continuously differentiable with f(O) = O, f' (O) #- O. It is proved that the local immunization is achieved and a formula for the immunizing duration is derived. Theorem 2 provides a formula for the immunizing duration of the portfolio combined with two cash flows. These two theorems extend validity of all similar type results presented by Bierwag (1983).