3 problems

Let $\xi(u,m)$ denote the value function for the minimum probability of drawdown, and let $\mathcal{H}^*_l(u)$ be the strategy specified by … Suppose the condition … holds for all…

Let $K$ be an allocation vector in the feasible set $\mathcal{K}$, let $D(K)$ denote the maximum drawdown, and let $P(D(K)\leq\varepsilon)$ denote the probability that the maximum…

Let $m^*<m<c/r$, and let $\pi^*(w,m)$ denote the optimal amount invested in the risky asset when wealth is $w$ and the drawdown level is $m$. Monotonicity conjecture. The first par…