Optimal investment with random endowments in incomplete markets

By Julien Hugonnier, Dmitry O. Kramkov. 2004

146 citations recorded by the source corpus.

In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization problem not only the initial capital but also the number of units of the random endowments. We show that this approach leads to a dual problem, whose solution is always attained in the space of random variables. In particular, this technique does not require the use of finitely additive measures and the related assumption that the endowments are bounded.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/2db524c62200966fad213e83fa80af6a2e2cd0ca

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Citations in the corpus

Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment (2005, methodology): “…by the less known notion of acceptability [introduced by Delbaen and Schachermayer (1997)], because admissibility is not adequate for dealing with nonbounded random endowment processes, as was shown in the context of utility maximization from terminal wealth by Hugonnier and Kramkov (2004).”
OPTIMAL INVESTMENT WITH AN UNBOUNDED RANDOM ENDOWMENT AND UTILITY‐BASED PRICING (2007, background): “Hugonnier and Kramkov (2004) consider an unbounded endowment (whose modulus is super-hedgeable) for a general utility function which is defined on the positive real line.”
Portfolio choice under dynamic investment performance criteria (2009, result): “If the terminal utility is taken to be state-dependent, VT (x;T ) 2 FT ; (see, for example, [12], [28] as well as [3], [6] and [10]), the traditional and new formulations are, essentially, identical in [0; T ] : We conclude by mentioning that there is a vast literature on the specication, construct”
ON UTILITY‐BASED PRICING OF CONTINGENT CLAIMS IN INCOMPLETE MARKETS (2005, unknown): “represents the maximal expected utility that an agent whose endowment is given by x units of cash and q units of the contingent claim can achieve by trading in the financial market, see [11].”
Option Pricing: Valuation Models and Applications (2004, unknown): “Problems of this nature are analyzed by Duffie et al. (1997), Cuoco (1997), Cvitani´c et al. (2001), Karatzas and Zitkovic (2003), and Hugonnier and Kramkov (2004), in continuous time settings.”
INDIFFERENCE PRICE WITH GENERAL SEMIMARTINGALES (2009, background): “ngale markets with random endowment (the reader is deferred to [BF06] and the literature therein for the case of no random endowment) and utility functions ﬁnite valued on R(see Hugonnier and Kramkov [HK04] and the literature therein for utility functions ﬁnite valued on R+). 2 The set up for utilit”
Sensitivity analysis of utility-based prices and risk-tolerance wealth processes (2006, methodology): “We study a financial framework similar to the one in [8], referring to this paper for more details and references.”
Forward-backward systems for expected utility maximization (2011, background): “It is known in this case is that an optimal strategy exists (see [16]) which is located in a much larger space than Πx.”