随机波动下 XVA 方程的温和经典解法

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2024-03-25 DOI:10.1137/22m1506882

Damiano Brigo, Federico Graceffa, Alexander Kalinin

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引用次数: 0

摘要

SIAM 金融数学期刊》，第 15 卷第 1 期，第 215-254 页，2024 年 3 月。摘要。我们将存在违约、抵押品和资金情况下的或有债权估值扩展到随机函数环境，并用马氏过程描述违约前价值过程。违约前价值半马尔廷模型也可以用随机路径依赖系数的 BSDE 和马廷格模型来描述。在此过程中，我们放宽了对可用市场信息的条件，并构建了一大类违约时间。此外，在随机波动性条件下，我们通过抛物线半线性 PDE 的温和解来描述违约前价值过程，并给出温和解唯一存在且经典的充分条件。

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Mild to Classical Solutions for XVA Equations under Stochastic Volatility

SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 215-254, March 2024.
Abstract. We extend the valuation of contingent claims in the presence of default, collateral, and funding to a random functional setting and characterize pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers. En route, we relax conditions on the available market information and construct a broad class of default times. Moreover, under stochastic volatility, we characterize pre-default value processes via mild solutions to parabolic semilinear PDEs and give sufficient conditions for mild solutions to exist uniquely and to be classical.

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.