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Moment-matching approximations for stochastic sums in non-Gaussian Ornstein–Uhlenbeck models

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  • Brignone, Riccardo
  • Kyriakou, Ioannis
  • Fusai, Gianluca

Abstract

In this paper, we recall actuarial and financial applications of sums of dependent random variables that follow a non-Gaussian mean-reverting process and contemplate distribution approximations. Our work complements previous related studies restricted to lognormal random variables; we revisit previous approximations and suggest new ones. We then derive moment-based distribution approximations for random sums attuned to Asian option pricing and computation of risk measures of random annuities. Various numerical experiments highlight the speed–accuracy benefits of the proposed methods.

Suggested Citation

  • Brignone, Riccardo & Kyriakou, Ioannis & Fusai, Gianluca, 2021. "Moment-matching approximations for stochastic sums in non-Gaussian Ornstein–Uhlenbeck models," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 232-247.
    • Handle: RePEc:eee:insuma:v:96:y:2021:i:c:p:232-247
    DOI: 10.1016/j.insmatheco.2020.12.002
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    More about this item

    Keywords

    Mean reversion; Non-Gaussian processes; Moment-matching; Asian option valuation; Stochastic annuities;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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