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Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities) are associated with distributions over them (second-order representations) have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions. [ABSTRACT FROM AUTHOR]

We consider an investor who wants to maximize expected utility of terminal wealth. Stock returns are modelled by a stochastic differential equation with non-constant coefficients. If the drift of the stock returns depends on some process independent of the driving Brownian motion, it may not be adapted to the filtration generated by the stock prices. In such a model with partial information, due to the non-constant drift, the position in the stocks varies between extreme long and short positions making these strategies very risky when trading on a daily basis. To reduce the corresponding shortfall risk, motivated by Cuoco, He and Issaenko [Operations Research, 2008, 56, pp. 358–368.] we impose a class of risk constraints on the strategy, computed on a short horizon, and then find the optimal policy in this class. This leads to much more stable strategies that can be computed for both classical drift models, a mean reverting Ornstein–Uhlenbeck process and a continuous-time Markov chain with finitely many states. The risk constraints also reduce the influence of certain parameters that may be difficult to estimate. We provide a sensitivity analysis for the trading strategy with respect to the model parameters in the constrained and unconstrained case. The results are applied to historical stock prices. [ABSTRACT FROM AUTHOR]

Empirical distributions are often claimed to be superior to parametric distributions, yet to also increase the computational complexity and are therefore hard to apply in portfolio optimization. In this paper, we approach the portfolio optimization problem under constraints on the portfolio’s Value at Risk and Expected Tail Loss, respectively, under empirical distributions for the Standard and Poor’s 100 stocks. We apply a heuristic optimization method which has been found to overcome the restrictions of traditional optimization techniques. Our results indicate that empirical distributions might turn into a Pandora’s Box: Though highly reliable for predicting the assets’ risks, employing these distributions in the optimization process might result in severe mis-estimations of the resulting portfolios’ actual risk. It is found that even a simple mean-variance approach can be superior despite its known specification errors. [ABSTRACT FROM AUTHOR]