Consumption-investment under alternative stochastic-integral conventions

Mario Ayala and Benjamin Vallejo Jim\'enez

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Abstract: We study the Merton consumption-investment problem when risky asset dynamics are written under stochastic-integral conventions indexed by $\alpha$, interpolating between the It\^o ($\alpha=0$), Stratonovich ($\alpha=1/2$), and H\"anggi-Klimontovich ($\alpha=1$) conventions. Transforming the drift jointly with the convention leaves the optimal policy unchanged; holding the drift coefficient numerically fixed changes the investor's opportunity set. Under logarithmic utility, consumption is unaffected while the optimal portfolio weight shifts by $\alpha V^{-1}d_V$; for a Heston asset, $\pi_t^\ast=\alpha+(\mu-r+\alpha\varrho\xi/2)/V_t$, which can change sign across volatility states. Identifying the convention from return data alone is impossible without additional structural restrictions.

Date: 2026-02, Revised 2026-10
New Economics Papers: this item is included in nep-upt
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