4 problems

Vanishing orthogonal-component conjecture. The components corresponding to the log-return Brownian motion vanish:

Let $U$ be an utility function satisfying the INADA conditions with $U(0+)=0$, let $\mathcal{X}(x)$ be the set of admissible wealth processes with initial capital $x$, and let…

Let $c^*$ and $\mathcal{W}^*$ be the optimal consumption and wealth processes, and let $Y$ be the process from the existence result. Define the optimal value process by … Let $f$ d…

Let $P_I$ denote the state price of the insurance, equivalently the insurance premium, in the model. Assume that $P_I$ is determined by no-arbitrage arguments in a frictionless ins…