A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization

Daniel Andersson () and Boualem Djehiche

Mathematical Methods of Operations Research, 2010, vol. 72, issue 2, 273-310

Abstract: We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a relaxed maximum principle. The main motivation is an optimal bond portfolio problem in a market where there exists a continuum of bonds and the portfolio weights are modeled as measure-valued processes on the set of times to maturity. Copyright Springer-Verlag 2010

Keywords: Stochastic control; Relaxed control; Maximum principle; $${\mathcal{H}}$$ -function; Bond portfolio; 93E20; 60H30; 60H10; 91B28 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s00186-010-0320-7

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