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Multivariate utility maximization with proportional transaction costs and random endowment

Benedetti, Giuseppe; Campi, Luciano (2012), Multivariate utility maximization with proportional transaction costs and random endowment, SIAM Journal on Control and Optimization, 50, 3, p. 1283-1308. http://dx.doi.org/10.1137/110831064

Type
Article accepté pour publication ou publié
Date
2012
Journal name
SIAM Journal on Control and Optimization
Volume
50
Number
3
Pages
1283-1308
Publication identifier
http://dx.doi.org/10.1137/110831064
Metadata
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Author(s)
Benedetti, Giuseppe
Campi, Luciano
Abstract (EN)
In this paper we deal with a utility maximization problem at finite horizon on a continuous-time market with conical (and time varying) constraints (particularly suited to model a currency market with proportional transaction costs). In particular, we extend the results in Campi and Owen (2011) to the situation where the agent is initially endowed with a random and possibly unbounded quantity of assets. We start by studying some basic properties of the value function (which is now defined on a space of random variables), then we dualize the problem following some convex analysis techniques which have proven very useful in this field of research. We finally prove the existence of a solution to the dual and (under an additional boundedness assumption on the endowment) to the primal problem. The last section of the paper is devoted to an application of our results to utility indifference pricing.
Subjects / Keywords
Utility-based pricing; Duality theory; Multivariate utility function; Optimal portfolio; Random endowment; Foreign exchange market; Transaction costs
JEL
G11 - Portfolio Choice; Investment Decisions

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