Dual representation of minimal supersolutions of convex BSDEs

Samuel Drapeau; Michael Kupper; Emanuela Rosazza Gianin; Ludovic Tangpi

doi:10.1214/14-AIHP664

Dual representation of minimal supersolutions of convex BSDEs

Samuel Drapeau, Michael Kupper, Emanuela Rosazza Gianin, Ludovic Tangpi

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We give a dual representation of minimal supersolutions of BSDEs with non-bounded, but integrable terminal conditions and under weak requirements on the generator which is allowed to depend on the value process of the equation. Conversely, we show that any dynamic risk measure satisfying such a dual representation stems from a BSDE. We also give a condition under which a supersolution of a BSDE is even a solution.

Original language	English (US)
Pages (from-to)	868-887
Number of pages	20
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	52
Issue number	2
DOIs	https://doi.org/10.1214/14-AIHP664
State	Published - May 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Cash-subadditive risk measures
Convex duality
Supersolutions of BSDEs

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10.1214/14-AIHP664

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AU - Drapeau, Samuel

AU - Kupper, Michael

AU - Rosazza Gianin, Emanuela

AU - Tangpi, Ludovic

N1 - Publisher Copyright: © Association des Publications de l'Institut Henri Poincaré, 2016.

PY - 2016/5

Y1 - 2016/5

N2 - We give a dual representation of minimal supersolutions of BSDEs with non-bounded, but integrable terminal conditions and under weak requirements on the generator which is allowed to depend on the value process of the equation. Conversely, we show that any dynamic risk measure satisfying such a dual representation stems from a BSDE. We also give a condition under which a supersolution of a BSDE is even a solution.

AB - We give a dual representation of minimal supersolutions of BSDEs with non-bounded, but integrable terminal conditions and under weak requirements on the generator which is allowed to depend on the value process of the equation. Conversely, we show that any dynamic risk measure satisfying such a dual representation stems from a BSDE. We also give a condition under which a supersolution of a BSDE is even a solution.

KW - Cash-subadditive risk measures

KW - Convex duality

KW - Supersolutions of BSDEs

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Dual representation of minimal supersolutions of convex BSDEs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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