2013/09/02 by Miklós Rásonyi, Rásonyi, Miklós, Andrea M. Rodrigues +1
Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #FOS: Economics and business #Financial Markets and Investment Strategies #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1309.0362
openalex publication_date 2013/09/02 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
This paper examines an optimal investment problem in a continuous-time\n(essentially) complete financial market with a finite horizon. We deal with an\ninvestor who behaves consistently with principles of Cumulative Prospect\nTheory, and whose utility function on gains is bounded above. The\nwell-posedness of the optimisation problem is trivial, and a necessary\ncondition for the existence of an optimal trading strategy is derived. This\ncondition requires that the investor's probability distortion function on\nlosses does not tend to 0 near 0 faster than a given rate, which is determined\nby the utility function. Under additional assumptions, we show that this\ncondition is indeed the borderline for attainability, in the sense that for\nslower convergence of the distortion function there does exist an optimal\nportfolio.\n