Shipping through the Strait of Hormuz under threat

Five statements about the model; the mapping to the strait is a reconstruction R, and no statement estimates any real loss, premium or escort requirement.

• A guarantee needs no reading of intentions. The value bounds the loss against every allocation of the threat's units, whatever their purpose, as long as the threat can bring no more than $A$ units to bear. In the base case the protector can hold the expected loss to $\frac{4}{3}$ of six ships, and a threat of that strength can impose $\frac{4}{3}$; a pooled cover priced from the guarantee breaks even at a per-transit rate of $\frac{2}{9}\lambda$. What the bound needs is capability — how many units can be brought to one window — not intent D [Proposition 9.16 (p. 381)(a)]; how capability maps to “units” is a reconstruction R.

• What costs is a visible draw, not a published policy. A fixed schedule loses $2$ ships against its best reply, and so does a rotating schedule whose realised assignment the threat sees before striking: the break-even rate rises by half, from $\frac{2}{9}\lambda$ to $\frac{1}{3}\lambda$. Publishing the mixture itself costs nothing in this zero-sum game D [Proposition 9.15 (p. 380)(b), Proposition 9.16 (p. 381)(a)]. This is Chapter 2's observability branch (Proposition 2.10 (p. 97)) and Chapter 6's revealed inspection (Proposition 6.4 (p. 254)) in the setting of escorts. In the record, the advisories' guidance on AIS transmission and the announcements of naval presence bear on this field of the card, field 3; how much they reveal of a day's allocation is an empirical question R.

• Unpredictability is worth something only against the middle of the three threats compared. With one strike unit the base plan loses nothing even when it is predictable; with three it loses $2$ whether it is predictable or not; only with two units is randomising worth $\frac{2}{3}$ of a ship D [Proposition 9.16 (p. 381)(a)]. The comparison is these three budgets, not a rule in the threat's strength: a rotation worth keeping against one level of threat may be worth nothing against another.

• Convoy or disperse: the ranking reverses with the escorts. Escorts lose nothing if and only if $E\ge kA$ D [Proposition 9.15 (p. 380)(a)]. Below that threshold the effect of spreading the six ships over more windows depends on where the escort budget stands: with three escorts more windows lower the loss ($\frac{3}{2}$ in two windows, $\frac{4}{3}$ in three, $1$ in six), but not below every budget. With four escorts the two-window plan is safe while three and six windows each lose $\frac{8}{9}$; with five the order is the reverse of the order with three: $0$, $\frac{2}{3}$, $\frac{7}{9}$ (tab:net-hormuz,fig:net-hormuz) D [Proposition 9.16 (p. 381)(b)]. Closing a lane, as when ships are advised away from the traffic separation scheme, forces fewer windows; whether that raises or lowers the guarantee depends on where the escort budget stands against $kA$. Windows in one lane share a failure, as routes through one chokepoint do in Model K4 (Definition 9.12 (p. 378)) R.

• A price that learns from transits learns slowly when transits are few. An insurer that revises its estimate of the probability of a hit from transits without incident moves at the speed of traffic: in Exercise 9.9 (p. 371) halving a prior estimate takes ten clean transits, half a day at twenty transits a day and five days at two. Low traffic slows the fall in price, and a high price keeps traffic low. The mechanism is consistent with the Secretary-General's remark that market pricing was not adjusting as conditions improved; it does not explain it, and other mechanisms — reserves set after losses, capacity withdrawn, correlated losses across a fleet — fit the remark as well S.

The threat is not one coordinated player with a fixed number of interchangeable units, and the contest is not decided by a count: interception is probabilistic, and some means of attack, such as mines, are standing hazards of a lane rather than moves in a period. A hazard that stops the whole passage whatever the escorts do lies outside the allocation game: it adds the same expected loss to every plan, leaves the best allocation unchanged short of a certain interruption — at which every allocation does equally badly — and shrinks in proportion what any protective choice is worth (Exercise 9.10 (p. 371)). Traffic is not fixed: in the record transits fell from about $58$ to a few a day, so shipowners' decisions to sail — driven by the premium, the charter and the crew's consent — are the largest response, and the model holds them constant. Escorts are not interchangeable, missions have different mandates and areas (close protection, guidance, mine clearance, awareness), and several protectors coordinate imperfectly, which is a problem of Chapter 8. The zero-sum payoff overstates the opposition of interests and ignores everything but ships: delay, crews' safety and the legal regime of passage are absent. Days are linked in fact, through learning by both sides, repairs and the clearing of mines. Insurance transfers the financial consequence of a loss under contract; it protects no ship.