On The Weak Representation Property in Progressively Enlarged\n Filtrations with an Application to Exponential Utility Maximization

2018/03/29 by Paolo Di Tella, Di Tella, Paolo · 1 citation
Economics, Econometrics and Finance · #60G46 #60G57 #60H05 #60H30 #Economic theories and models #FOS: Mathematics #Financial Markets and Investment Strategies #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1803.10939

openalex publication_date 2018/03/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper we show that the weak representation property of a\nsemimartingale X with respect to a filtration mathbbF is preserved in\nthe progressive enlargement mathbbG by a random time \τ avoiding\n mathbbF-stopping times and such that mathbbF is immersed in\n mathbbG. As an application of this, we can solve an exponential utility\nmaximization problem in the enlarged filtration mathbbG following the\ndynamical approach, based on suitable BSDEs, both over the fixed time horizon\n[0,T], T>0, and over [0,T wedge\τ].\n

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• 2BSDE with uncertain horizon and application to stochastic control in erratic environments

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