The optimal investment problem in stochastic and local volatility models

Vladimir Piterbarg

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We revisit the classical Merton optimal allocation problem.
We consider local and stochastic volatility models.
Significant corrections to the Merton ratio arise from hard to observe behavior of the variance process around zero.
Having corrected the dynamics of the variance process around zero we show that the adjustment to the myopic Merton ratio can be largely deduced from observed option prices.
This paves the way to a practical approach to a more efficient asset allocation.

Abstract

We revisit the classical Merton optimal allocation problem and show that significant corrections to the Merton ratio arise from the hard-to-observe behavior of the volatility process around zero. Having regularized this behavior, we show that the adjustment to the “myopic” Merton ratio can be largely deduced from observed option prices, which paves the way for a practical approach to more efficient asset allocation.

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