Extreme Events and Portfolio Construction [18]

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Bullet points include: Maximum likelihood estimation (MLE) has nice theoretical properties, e.g. asymptotically efficient and unbiased. A potentially attractive way of targeting a good fit in the tail is thus to: Re-express the overall likelihood function to relate to ordered observations. Differentially weight contributions from individual observations to this (re-expressed) likelihood function, giving greater weight to observations more obviously in the relevant tail. Gives same answer as traditional MLE in the special case where all observations are given equal weight. Maybe also allow for time-varying volatility by including in the problem specification an autocorrelation parameter?

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