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In this paper, we study a utility maximization problem with random horizon and reduce it to the analysis of a specific backward stochastic differential equation (BSDE), which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

The paper analyzes risk assessment for cash flow processes in continuous time. We combine the framework of convex risk measures for processes with a decomposition result for optional and predictable measures to provide a systematic approach to the issues of model ambiguity and uncertainty about the time value of money. We also establish a link between risk measures for processes and BSDEs. [ABSTRACT FROM AUTHOR]

Abstract: We extend the work of Delong and Imkeller (2010)  concerning backward stochastic differential equations with time delayed generators (delay BSDEs). We give moment and a priori estimates in general -spaces and provide sufficient conditions for the solution of a delay BSDE to exist in . We introduce decoupled systems of SDEs and delay BSDEs (delay FBSDEs) and give sufficient conditions for their variational differentiability. We connect these variational derivatives to the Malliavin derivatives of delay FBSDEs via the usual representation formulas. We conclude with several path regularity results, in particular we extend the classic -path regularity to delay FBSDEs. [Copyright &y& Elsevier]

Abstract: In this paper we deal with the utility maximization problem with general utility functions including power utility with liability. We derive a new approach in which we reduce the resulting control problem to the study of a system of fully-coupled Forward–Backward Stochastic Differential Equations (FBSDEs) that promise to be accessible to numerical treatment. [Copyright &y& Elsevier]