Backward stochastic differential equations and partial differential equations with quadratic growth

By M. Kobylanski. 2000

862 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/704ed50372ad15c6677608e3e9c40dd42f75b1f8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. P. Briand
2. Adrien Richou
3. Ying Hu
4. Romuald Elie
5. Gordan vZitkovi'c
6. Hao Xing
7. Shige Peng
8. Freddy Delbaen

In Computational Theory and Mathematics

1. Adrien Richou
2. Shige Peng
3. Romuald Elie
4. Huyen Pham
5. Jianfeng Zhang
6. Ying Hu
7. Freddy Delbaen
8. P. Briand

In Finance

1. Adrien Richou
2. Jianfeng Zhang
3. P. Briand
4. Shige Peng
5. Romuald Elie
6. Huyen Pham
7. Nizar Touzi
8. Ying Hu

Citations in the corpus

• Weak Solutions of Forward–Backward SDE's (2003, background): “We refer to [1,9,13,17,19,21,27–29,32,33], and the book [23] for the wellposedness of various forms of such equations.”
• Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, background): “The second one is also the existence and uniqueness theorem, in which g satisfies quadratic growth condition in z and some local Lipschitz conditions, obtained by Kobylanski (2000) for the case where the terminal value ξ is bounded.”
• Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursiv (2003, neutral): “Further existence results have been developed by Lepeltier and San Mart n (1997), Kobylanski (2000), and Lepeltier and San Mart n (2002).”
• Smooth Ambiguity Aversion toward Small Risks and Continuous-Time Recursive Utility (2013, methodology): “BSDE existence and uniqueness results, based on the type of Lipschitz-growth assumptions on the driver familiar from SDE theory, were …rst obtained by Pardoux and Peng (1990) and Du¢ e and Epstein (1992) (see also El Karoui, Peng, and Quenez (1997) and El Karoui and Mazliak (1997)).”
• A simple constructive approach to quadratic BSDEs with or without delay (2013, methodology): “Theorem 2.1 [Kobylanski [11]] If (H0) and (Hq) hold, then the BSDE (2.1) has a unique solution (Y,Z) ∈ S∞ ×H2.”
• On some recent aspects of stochastic control and their applications (2005, background): “Some extensions to the quadratic growth case are studied in [52] and more recently in [42].”
• Exponential Utility Maximization in an Incomplete Market with Defaults (2011, methodology): “Note that the proof of this result (see [26]) is based on similar arguments as those used in the proof of the monotone stability convergence theorem for quadratic BSDEs of Kobylanski [20].”
• Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition (2011, neutral): “In the first one [21], Kobylanski obtains an existence and uniqueness result for quadratic BSDEs when the terminal condition is bounded.”
• Numerical simulation of quadratic BSDEs (2013, neutral): “Existence and uniqueness of solution for such BSDEs has been first proved by Kobylanski [34].”
• Numerical simulation of BSDEs with drivers of quadratic growth (2010, background): “Many papers deal with existence and uniqueness of solution for such BSDEs; we refer the reader to [17, 18] when the terminal condition is bounded and [3, 4, 9] for the unbounded case.”