In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that dynamic risk measures are subject to horizon risk, so we propose to use the fully dynamic version. To quantify horizon risk, we introduce h-longevity as an indicator. We investigate these notions together with other properties of risk measures, such as normalization, restriction property, and different formulations of time-consistency. We also consider these concepts for fully dynamic risk measures generated by backward stochastic differential equations (BSDEs), backward stochastic Volterra integral equations (BSVIEs), and families of these. Within this study, we provide new results for BSVIEs, such as a converse comparison theorem and the dual representation of the associated risk measures.

Di Nunno, G., Rosazza Gianin, E. (2024). Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 15(2), 399-435 [10.1137/23m1546804].

Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs

Rosazza Gianin, E
2024

Abstract

In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that dynamic risk measures are subject to horizon risk, so we propose to use the fully dynamic version. To quantify horizon risk, we introduce h-longevity as an indicator. We investigate these notions together with other properties of risk measures, such as normalization, restriction property, and different formulations of time-consistency. We also consider these concepts for fully dynamic risk measures generated by backward stochastic differential equations (BSDEs), backward stochastic Volterra integral equations (BSVIEs), and families of these. Within this study, we provide new results for BSVIEs, such as a converse comparison theorem and the dual representation of the associated risk measures.
Articolo in rivista - Articolo scientifico
fully dynamic risk measures, time-consistency, BSDEs, BSVIEs, converse comparison theorem for BSVIEs, dual representation, horizon risk, h-longevity
English
2024
15
2
399
435
none
Di Nunno, G., Rosazza Gianin, E. (2024). Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 15(2), 399-435 [10.1137/23m1546804].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/478640
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