Multivariate utility maximization with proportional transaction costs and random endowment (Q2910904)

The authors consider a stochastic optimization problem resulting from maximization of utility at a fixed terminal horizon for a continuous-time market with proportional transaction costs. The agent's preferences are defined by a multivariate utility function which satisfies some assumptions including strict concavity, essential smoothness and asymptotic satiability. The agent trades in all available assets in order to reach the objective. The authors propose a generalization of the results of \textit{L. Campi} and \textit{M. P. Owen} [``Multivariate utility maximization with proportional transaction costs'', Finance Stoch. 15, No. 3, 461--499 (2011; \url{doi:10.1007/s00780-010-0125-9})] by allowing for a random and possibly unbounded quantity of initial assets. Market constraints and frictions are described by cone-valued processes. To prove the existence of a solution, the authors apply convex analysis tools which enable finding some sufficient conditions for the dual problem and ultimately also for the primal problem under some additional boundedness assumptions. As an example of application of the results, utility-based pricing of contingent claims [\textit{M. P. Owen} and \textit{G. Žitković}, Math. Finance 19, No. 1, 129--159 (2009; Zbl 1155.91393)] is considered.