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Title: Building Robust Control Barrier Functions from Robust Maximal Output Admissible Sets
Award ID(s):
2411667
PAR ID:
10624015
Author(s) / Creator(s):
;
Publisher / Repository:
IEEE
Date Published:
ISSN:
2576-2370
ISBN:
979-8-3503-1633-9
Page Range / eLocation ID:
8171 to 8177
Format(s):
Medium: X
Location:
Milan, Italy
Sponsoring Org:
National Science Foundation
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  2. Abstract We introduce an arbitrage‐free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the exact return rate of her counterparty's bond, but she knows it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the super‐replicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the closeout value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA. 
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