具有奇异终端值的BSDE发电机的生长条件，保证其一直持续到终端时间

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-01-31 DOI:10.1016/j.spa.2025.104588

Dorian Cacitti-Holland, Laurent Denis, Alexandre Popier

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引用次数: 0

摘要

研究了一类后向随机微分方程解在端点条件为奇异时的极限行为，即它可以正概率地等于无穷。在马尔可夫条件下，Malliavin的演算使我们能够证明，如果在发电机的增长w.r.t.y和增长w.r.t.z之间的平衡条件满足，则可以证明连续性。据我们所知，这种情况是新的。将所得结果应用于金融流动性问题和一类半线性偏微分方程的求解；强加的假设在PDE的文献中也是新的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time

We study the limit behavior of the solution of a backward stochastic differential equation when the terminal condition is singular, that is it can be equal to infinity with a positive probability. In the Markovian setting, Malliavin’s calculus enables us to prove continuity if a balance condition between the growth w.r.t.

y

and the growth w.r.t.

z

of the generator is satisfied. As far as we know, this condition is new. We apply our result to liquidity problem in finance and to the solution of some semi-linear partial differential equation ; the imposed assumption is also new in the literature on PDE.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.