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Contents of PMS, Vol. 38, Fasc. 8,
pages 139 - 155
DOI: 10.19195/0208-4147.38.1.8
 

BELLMAN EQUATIONS FOR TERMINAL UTILITY MAXIMIZATION WITH GENERAL BID AND ASK PRICES

Tomasz Rogala
Łukasz Stettner

Abstract: In the paper we solve a system of Bellman equations for finite horizon continuous time terminal utility maximization problem with general cądląg bid and ask prices. We assume that we have a restricted number of transactions at time moments we choose. The main result of the paper says that we can find a regular version of solutions to the system of Bellman equations, which enables us to find the form of nearly optimal strategies.

2010 AMS Mathematics Subject Classification: Primary: 93E20; Secondary: 91G10, 60G07.

Keywords and phrases: Bellman equation, bid and ask prices, optimal stopping, terminal utility maximization.

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