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A New Stochastic Fubini-Type Theorem

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  • Michael Heinrich Baumann

    (University of Bayreuth)

Abstract

When a stochastic process is given through an Itō integral, i.e. a stochastic integral, or a stochastic differential equation (SDE), an analytical solution does not have to exist—and even if there is a closed-form solution, the derivation of this solution can be very complex. When the solution of the stochastic process is not needed but only the expected value as a function of time, the question arises whether it is possible to use the expectation operator directly on the stochastic integral or on the SDE and to somehow calculate the expectation of the process as a Riemann integral over the expectation of the integrands and integrators. In this paper, we show that if the integrator is linear in expectation, the expectation operator and an Itō integral can be interchanged. Additionally, we state how this can be used on SDEs and provide an application from the field of technical trading, i.e. from the field of mathematical finance.

Suggested Citation

  • Michael Heinrich Baumann, 2021. "A New Stochastic Fubini-Type Theorem," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 408-420, February.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:1:d:10.1007_s13171-019-00195-y
    DOI: 10.1007/s13171-019-00195-y
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    References listed on IDEAS

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    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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    Cited by:

    1. Michael Heinrich Baumann, 2022. "Beating the market? A mathematical puzzle for market efficiency," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 279-325, June.

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