BSDEs and applications. (English) Zbl 1168.60030
Carmona, René (ed.) et al., Indifference pricing: Theory and applications. Princeton, NJ: Princeton University Press (ISBN 978-0-691-13883-1/hbk). Princeton Series in Financial Engineering, 267-320 (2009).
This paper is a wide survey on backward stochastic differential equations (BSDEs) and their applications. Let us remember that these equations have been widely used in stochastic control and mathematical finance.
The paper begins studying the problem of the existence and uniqueness of a solution, considering one-dimensional linear BSDEs and one-dimensional BSDEs with non-lipschitz coefficients. The second section is devoted to the applications to optimization problems: financial mathematics, an optimal control problem and the study of zero-sum stochastic differential games. In the third section, the authors deal with Markovian BSDEs, studying the viscosity solution of semilinear PDEs and general regularity results on BSDEs. In section 4, they consider BSDEs with quadratic growth with their applications in risk-sensitive control. The last section is devoted to reflected BSDEs: with one reflecting barrier and with two reflecting barriers.
For the entire collection see [Zbl 1155.91008].
The paper begins studying the problem of the existence and uniqueness of a solution, considering one-dimensional linear BSDEs and one-dimensional BSDEs with non-lipschitz coefficients. The second section is devoted to the applications to optimization problems: financial mathematics, an optimal control problem and the study of zero-sum stochastic differential games. In the third section, the authors deal with Markovian BSDEs, studying the viscosity solution of semilinear PDEs and general regularity results on BSDEs. In section 4, they consider BSDEs with quadratic growth with their applications in risk-sensitive control. The last section is devoted to reflected BSDEs: with one reflecting barrier and with two reflecting barriers.
For the entire collection see [Zbl 1155.91008].
Reviewer: Carles Rovira (Barcelona)
