Jensen’s Inequality for Backward Stochastic Differential Equations*

Abstract

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen’s inequality for g- expectation in [4, 7–9].

Keywords

Backward stochastic differential equation / g-Expectation / Jensen’sinequality for g-expectation / Jensen’s inequality for BSDEs / 60H10

References

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