Transport cost benefit analysis, when properly done, takes account of the benefits arising from increased transport demand induced by lower transport costs, and these benefits are typically evaluated by the rule-of-one-half or the trapezium rule. This states that the transport gain is the average level of transport services times the fall in transport costs, Σ–2 (qi′ + qi).(-∆ti), where qi is t...

Given a stochastic state process $(X_t)_t$ and real-valued submartingale cost $(S_t)_t$, we characterize optimal stopping times $\tau$ that minimize the expectation of $S_\tau$ while realizing given initial target distributions $\mu$ $\nu$, i.e., $X_0\sim \mu$ $X_\tau \sim \nu$. A dual optimization problem is considered shown to be attained under suitable conditions. The solution then provides ...