Robust utility maximisation with intractable claims

Yunhong Li (), Zuo Quan Xu () and Xun Yu Zhou ()
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Yunhong Li: The Hong Kong Polytechnic University
Zuo Quan Xu: The Hong Kong Polytechnic University
Xun Yu Zhou: Columbia University

Finance and Stochastics, 2023, vol. 27, issue 4, No 7, 985-1015

Abstract: Abstract We study a continuous-time expected utility maximisation problem where the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution; hence the name “intractable claim”. In view of the lack of necessary information about the claim, we consider a robust formulation to maximise her utility in the worst scenario. We apply the quantile formulation to solve the problem, express the quantile function of the optimal terminal investment income as the solution of certain variational inequalities of ordinary differential equations, and obtain the resulting optimal trading strategy. In the case of exponential utility, the problem reduces to a (non-robust) rank-dependent utility maximisation with probability distortion whose solution is available in the literature. The results can also be used to determine the utility indifference price of the intractable claim.

Keywords: Intractable claim; Robust model; Quantile formulation; Calculus of variations; Variational inequalities; Rank-dependent utility; 91B28; 91G10; 35Q91 (search for similar items in EconPapers)
JEL-codes: C02 C61 C72 G11 G12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00780-023-00512-2

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