10 problems

The superhedging sets are subsets of $\mathbb{L}^2$ spaces indexed by time, and their approximate versions satisfy a set-valued Bellman's principle relating approximate superhedgin…

Let $Y_t$ denote the risky position, let $y_\star$ be the perfect target, and let $y_-<y_\star<y_+$ be boundary levels. Trading incurs transaction costs, and admissible strategies…

Let $\widetilde\pi_-$ and $\widetilde\pi_+$ be the lower and upper shadow-market trading boundaries, let $\Lambda$ be the target proportion, let $\gamma$ be the risk-aversion param…

Let $\widetilde\pi_-$ and $\widetilde\pi_+$ denote the lower and upper trading boundaries in the shadow market, and let $\varepsilon$ be the transaction-cost parameter. The compari…

Consider an optimal trading strategy in the option-pricing model with transaction costs, depending on the time $t$ and stock price $S$. In the corresponding model without transacti…

Let $Q_j(t,y,S)$ satisfy the transaction-cost pricing equation … On the domain $[0,T]\times\mathbb{R}\times\mathbb{R}^{+}$, the equation divides the space into three regions. Davis…

Let $S=(S_t)_{0\leq t\leq T}$ be a continuous, strictly positive semimartingale in a market with transaction-cost level $0<\lambda<1$. For every $0<\mu<\lambda$, suppose there exis…

No-trade interval conjecture. The no-trade region is given by an interval $[y_-,y_+]$ for some endpoints $y_-$ and $y_+$. This conjecture extends the familiar interval-shaped no-tr…

Linear vector optimisation conjecture. The constructions presented in the paper should be adaptable so that linear vector optimisation methods can be used to price and hedge both t…

A shadow price is a frictionless price process lying within the bid-ask spread and yielding the same optimal utility as the original market with transaction costs. Shadow-price exi…