Intertemporal hedging demand ($y^{\ast }=-[V_w\ell +{\sigma }_{\mathrm{state}}{V}_{w\mathrm{state}}]/V_{ww}$)

Intertemporal hedging demand adjusts the myopic risky position when investment opportunities depend on a stochastic state. Shared noise between wealth and that state contributes a cross derivative to the Hamilton-Jacobi-Bellman equation. In a complete diffusion market the optimal exposures combine the myopic market price of risk term and the value-gradient hedge term.