Timing in the presence of directional predictability: optimal stopping of skew Brownian motion

Luis H. R. Alvarez E, Paavo Salminen

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    7 Citations (Scopus)

    Abstract

    We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional predictability modeled by the presence of a skew point for the underlying has a nontrivial and somewhat surprising impact on the timing incentives of the decision maker. We prove that waiting is always optimal at the skew point for a large class of exercise payoffs. An interesting consequence of this finding, which is in sharp contrast with studies relying on ordinary Brownian motion, is that the exercise region for the problem can become unconnected even when the payoff is linear. We also establish that higher skewness increases the incentives to wait and postpones the optimal timing of an investment opportunity. Our general results are explicitly illustrated for a piecewise linear payoff.
    Original languageUndefined/Unknown
    Pages (from-to)377–400
    Number of pages24
    JournalMathematical Methods of Operations Research
    Volume86
    Issue number2
    DOIs
    Publication statusPublished - 2017
    MoE publication typeA1 Journal article-refereed

    Keywords

    • Skew Brownian motion
    • Excessive function
    • Martin representation
    • irreversible investment
    • optimal stopping

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