Completeness of security markets and backward stochastic differential equations with unbounded coefficients

2005 ◽  
Vol 63 (5-7) ◽  
pp. e2079-e2089 ◽  
Author(s):  
J. Yong
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Unbounded Coefficients ◽  
Security Markets

Integrability of exponential process and its application to backward stochastic differential equations

2018 ◽  
Vol 30 (4) ◽  
pp. 335-365
Author(s):  
Bujar Gashi ◽  
Jiajie Li
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Investment ◽  
Backward Stochastic Differential Equations ◽  
Type Condition ◽  
Unbounded Coefficients ◽  
Exponential Process ◽  
Market Completeness ◽  
Integrability Problem ◽  
Weaker Conditions

Abstract We consider the integrability problem of an exponential process with unbounded coefficients. The integrability is established under weaker conditions of Kazamaki type, which complements the results of Yong obtained under a Novikov type condition. As applications, we consider the solvability of linear backward stochastic differential equations (BSDEs) and market completeness, the solvability of a Riccati BSDE and optimal investment, all in the setting of unbounded coefficients.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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