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SENSITIVITY ANALYSIS OF NONLINEAR BEHAVIOR WITH DISTORTED PROBABILITY
Author(s) -
Cao XiRen,
Wan Xiangwei
Publication year - 2017
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12076
Subject(s) - sensitivity (control systems) , probability measure , expected utility hypothesis , mathematical optimization , derivative (finance) , measure (data warehouse) , nonlinear system , portfolio , incomplete markets , portfolio optimization , computer science , mathematics , econometrics , mathematical economics , economics , statistics , electronic engineering , engineering , physics , quantum mechanics , neoclassical economics , database , financial economics
In this paper, we propose a sensitivity‐based analysis to study the nonlinear behavior under nonexpected utility with probability distortions (or “distorted utility” for short). We first discover the “monolinearity” of distorted utility, which means that after properly changing the underlying probability measure, distorted utility becomes locally linear in probabilities, and the derivative of distorted utility is simply an expectation of the sample path derivative under the new measure. From the monolinearity property, simulation algorithms for estimating the derivative of distorted utility can be developed, leading to gradient‐based search algorithms for the optimum of distorted utility. We then apply the sensitivity‐based approach to the portfolio selection problem under distorted utility with complete and incomplete markets. For the complete markets case, the first‐order condition is derived and optimal wealth deduced. For the incomplete markets case, a dual characterization of optimal policies is provided; a solvable incomplete market example with unhedgeable interest rate risk is also presented. We expect this sensitivity‐based approach to be generally applicable to optimization problems involving probability distortions.