scholarly journals A note on rough differential equations with unbounded coefficients

2019 ◽  
Author(s):  
Yuzuru Inahama
Keyword(s):  
Differential Equations ◽  
Unbounded Coefficients

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.

scholarly journals The Cauchy-Dirichlet Problem for a Class of Linear Parabolic Differential Equations with Unbounded Coefficients in an Unbounded Domain

2011 ◽  
Vol 2011 ◽  
pp. 1-35 ◽  
Author(s):  
Gerardo Rubio
Keyword(s):  
Dirichlet Problem ◽  
Differential Equations ◽  
Parabolic Partial Differential Equations ◽  
Bounded Domains ◽  
Regular Boundary ◽  
Parabolic Differential Equations ◽  
Unbounded Coefficients ◽  
Connected Set ◽  
Locally Lipschitz ◽  
Uniform Ellipticity

We consider the Cauchy-Dirichlet problem in [0,∞)×D for a class of linear parabolic partial differential equations. We assume that D⊂ℝd is an unbounded, open, connected set with regular boundary. Our hypotheses are unbounded and locally Lipschitz coefficients, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution to the nonhomogeneous Cauchy-Dirichlet problem using stochastic differential equations and parabolic differential equations in bounded domains.

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