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RECURSIVE BACKWARD SCHEME FOR THE SOLUTION OF A BSDE WITH A NON LIPSCHITZ GENERATOR

Published online by Cambridge University Press:  05 January 2017

Paola Tardelli
Paola Tardelli*
Affiliation:
Department of Industrial and Information Engineering and Economics, University of L'Aquila, Piazzale E. Pontieri 1, 67040, Monteluco di Roio, Italy E-mail: [email protected]
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Abstract

On an incomplete financial market, the stocks are modeled as pure jump processes subject to defaults. The exponential utility maximization problem is investigated characterizing the value function in term of Backward Stochastic Differential Equations (BSDEs), driven by pure jump processes. In general, in this setting, there is no unique solution. This is the reason why, the value function is proven to be the limit of a sequence of processes. Each of them is the solution of a Lipschitz BSDE and it corresponds to the value function associated with a subset of bounded admissible strategies. Given a representation of the jump processes driving the model, the aim of this note is to give a recursive backward scheme for the value function of the initial problem.

Keywords

backward stochastic differential equationsdefaultincomplete market
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 2 , April 2017 , pp. 207 - 225
Copyright
Copyright © Cambridge University Press 2017 

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