کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1156721 958860 2013 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Second order backward stochastic differential equations with quadratic growth
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Second order backward stochastic differential equations with quadratic growth
چکیده انگلیسی

We extend the well posedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2012)  [31] to the case of a bounded terminal condition and a generator with quadratic growth in the zz variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman–Kac formula and a probabilistic representation for fully non-linear PDEs in this setting.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 123, Issue 10, October 2013, Pages 3770–3799
نویسندگان
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