Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 19 (2014), paper no. 38, 13 pp.
Continuous-Time Portfolio Optimisation for a Behavioural Investor with Bounded Utility on Gains
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose utility function on gains is bounded above. The well-posedness of the optimisation problemis trivial, and a necessary condition for the existence of an optimal trading strategyis derived. This condition requires that the investor’s probability distortion function on losses does not tend to 0 near 0 faster than a given rate, which is determined by the utility function. Under additional assumptions, we show that this condition is indeed the borderline for attainability, in the sense that for slower convergence of the distortion function there does exist an optimal portfolio.
Electron. Commun. Probab., Volume 19 (2014), paper no. 38, 13 pp.
Accepted: 23 June 2014
First available in Project Euclid: 7 June 2016
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Rásonyi, Miklós; Meireles Rodrigues, Andrea. Continuous-Time Portfolio Optimisation for a Behavioural Investor with Bounded Utility on Gains. Electron. Commun. Probab. 19 (2014), paper no. 38, 13 pp. doi:10.1214/ECP.v19-2990. https://projecteuclid.org/euclid.ecp/1465316740