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3 results

  • 6 - Continuous-Time Systems: Probabilistic Input Uncertainty

  • Alejandro D. Domínguez-García, University of Illinois, Urbana-Champaign
  • Book:
    Large-Scale System Analysis Under Uncertainty
    Published online:
    17 January 2022
    Print publication:
    17 February 2022, pp 166-201

  • Summary

    This chapter studies continuous-time dynamical systems described by a continuous-time state-space model whose input is subject to probabilistic uncertainty. The first part of the chapter is devoted to the analysis of linear systems and provides techniques for computing the first and second moments of the state vector when the evolution of the input vector is governed by a "white noise" process with known mean and covariance functions. Then, by additionally imposing this white noise process to be Gaussian, we provide a partial differential equation whose solution yields the pdf of the state vector. The second part of the chapter extends these techniques to the analysis of nonlinear systems, with a special focus on the case when the white noise governing the evolution of the input vector is Gaussian. The third part of the chapter illustrates the application of the techniques developed to the analysis of inertia-less AC microgrids when the measurements utilized by the frequency control system are corrupted by additive disturbances.

  • A portfolio of endowment policies and its limiting distribution

  • Gary Parker
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 26 / Issue 1 / May 1996
    Published online by Cambridge University Press:
    29 August 2014, pp. 25-33
    Print publication:
    May 1996
    • Article
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  • Two methods for approximating the limiting distribution of the present value of the benefits of a portfolio of identical endowment insurance contracts are suggested. The model used assumes that both future lifetimes and interest rates are random. The first method is similar to the one presented in Parker (1994b). The second method is based on the relationship between temporary and endowment insurance contracts.

  • Two Stochastic Approaches for Discounting Actuarial Functions

  • Gary Parker
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 24 / Issue 2 / November 1994
    Published online by Cambridge University Press:
    29 August 2014, pp. 167-181
    Print publication:
    November 1994
    • Article
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  • Two approaches used to model interest randomness are presented. They are the modeling of the force of interest accumulation function and the modeling of the force of interest. The expected value, standard deviation and coefficient of skewness of the present value of annuities-immediate are presented as illustrations. The implicit behavior of the force of interest under the two approaches is investigated by looking at a particular conditional expectation of the force of interest accumulation function.