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The stochastic stability of interest rates with jump changes. (English. Ukrainian original) Zbl 0990.60059

Theory Probab. Math. Stat. 61, 161-172 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 152-163 (2000).
The authors study the stochastic stability of interest rates with jumps. First of all, they investigate stochastic stability of the classical stochastic models of the interest rates, namely, Vasiček, Cox-Ross-Ingersoll and generalized Cox-Ross-Ingersoll models. Then these models of interest rates are considered with jumps and the stochastic stability is proved for such models of interest rates. Stochastic stability with probability 1, stability in mean, and mean-square stability are investigated for such models of interest rates with jumps. The method of random time change is used.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G30 Interest rates, asset pricing, etc. (stochastic models)
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