Fair risk allocation in illiquid markets

•Consider a firm having some divisions which have invested into some illiquid assets.•Using coherent measures of risk there is some diversification benefit to be allocated.•We use cooperative game theory and simulations to assess fair risk capital allocation.•We consider Core Compatibility, Equal Treatment Property, and Strong Monotonicity.•We show the impossibility to satisfy those three fairness notions at the same time.

Let us consider a financial firm having some divisions which have invested into some risky assets. Using coherent measures of risk there is some diversification benefit that should be allocated somehow. We use cooperative game theory and simulations to assess the possibility to jointly satisfy three inherent fairness requirements for allocating risk capital in illiquid markets: Core Compatibility, Equal Treatment Property, and Strong Monotonicity. We show that practically it is not possible to allocate risk in illiquid markets satisfying the three fairness notions at the same time, one has to give up at least one of them.