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A scaling limit for utility indifference prices in the discretised Bachelier model

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Listed:
  • Asaf Cohen

    (University of Michigan)

  • Yan Dolinsky

    (Hebrew University)

Abstract

We consider the discretised Bachelier model where hedging is done on a set of equidistant times. Exponential utility indifference prices are studied for path-dependent European options, and we compute their non-trivial scaling limit for a large number of trading times n $n$ and when risk aversion is scaled like n ℓ $n\ell $ for some constant ℓ > 0 $\ell >0$ . Our analysis is purely probabilistic. We first use a duality argument to transform the problem into an optimal drift control problem with a penalty term. We further use martingale techniques and strong invariance principles and obtain that the limiting problem takes the form of a volatility control problem.

Suggested Citation

  • Asaf Cohen & Yan Dolinsky, 2022. "A scaling limit for utility indifference prices in the discretised Bachelier model," Finance and Stochastics, Springer, vol. 26(2), pages 335-358, April.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:2:d:10.1007_s00780-022-00473-y
    DOI: 10.1007/s00780-022-00473-y
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    References listed on IDEAS

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    More about this item

    Keywords

    Utility indifference; Strong approximations; Path-dependent SDEs; Asymptotic analysis;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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