Monotone utility convergence

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We show that the maximal expected utility satisfies a monotone continuity property with respect to increasing information. Let be a sequence of increasing filtrations converging to , and let u n (x) and u ∞(x) be the maximal expected utilities when investing in a financial market according to strategies adapted to and , respectively. We give sufficient conditions for the convergence u n (x) → u ∞(x) as n → ∞. We provide examples in which convergence does not hold. Then we consider the respective utility-based prices, π n and π∞, of contingent claims under (G t n ) and (G t ∞). We analyse to what extent π n → π∞ as n → ∞.