5 problems

Let $U(x,y)=\log x+h(y)$ on $\mathbb{R}_+\times\mathbb{R}$, where $h$ is bounded and continuous with $m\leq h(y)\leq 1$ for some $m\in(0,1)$. Let $V(x,y)$ be the value function of…

Let $U(x,y)=x^{\alpha}U(1,y)$ be the utility function, and let $V(x,y)$ be the value function, bounded with respect to $y$. Let $\rho$, $\tau$, $\gamma$, and $\alpha$ be the model…

Let $t$ denote time and $x>0$ wealth, with $V(t,x)$ the equilibrium value function and $\widetilde{V}^{(k)}(t,x)$ the auxiliary functions indexed by $k\in\mathbb{N}$. In the unit-r…

Let $t$ denote time and $x$ wealth, with $V(t,x)$ the equilibrium value function and $\widetilde{V}^{(k)}(t,x)$ the auxiliary functions indexed by $k\in\mathbb{N}$. The model has r…

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…