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Decisions under uncertainty

Three chapters where you decide before you know: the quantile rule, tail risk optimised with an LP, and the duality that prices financial instruments.

  • The newsvendor

    The critical quantile rule, the scenario formulation and the value of the stochastic solution.

    Stochastic LP

  • VaR and CVaR

    Measuring the tail of the loss distribution and optimising it with the linear Rockafellar–Uryasev formulation.

    Scenario LP

  • Arbitrage and pricing

    Detecting an arbitrage is an LP; the duals are the risk-neutral probabilities that price every security.

    LP