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QVI characterization of contingent options in marine mutual insurance

As compared to a commercial insurance firm, a mutual insurance organization, such as a Protection & Indemnity Club (i.e., a P&I Club) in maritime insurance, adopts a none principal-agent mechanism of incentives, which mainly comprises two contingent options (impulse control), namely, contingent calls and refunds. We develop a band-type contingent option (BTCO) model for mutual insurance, and derive QVI (quasi-variational inequality) characteristics for the optimality of a BTCO policy which was introduced for cash management by Constantinides and Richard (Operations Research 26(4) (1978), 620-636). We show that an optimal BTCO policy can be determined by solving a boundary-value problem that is constructed with the QVI- characteristics. Finally, the QVI-based solution method is tested with numerical examples of mutual insurance management. With these findings, we argue that contingent options constitute an alternative incentive scheme that preserves the revelation principle under a non-principal-agent setting.