No abstract

No abstract

In this paper, we consider the problem of finding optimal portfolios in cases when the underlying probability model is not perfectly known. For the sake of robustness, a maximin approach is applied which uses a "confidence set" for the probability distribution. The approach shows the tradeoff between return, risk and robustness in view of the model ambiguity. As a consequence, a monetary value of information in the model can be determined.

No abstract

A stochastic version of the branch and bound method is proposed for solving stochastic global optimization problems. The method, instead of deterministic bounds, uses stochastic upper and lower estimates of the optimal value of subproblems, to guide the partitioning process. Almost sure convergence of the method is proved and random accuracy estimates derived. Methods for constructing random bounds for stochastic global optimization problems are discussed. The theoretical considerations are illustrated with an example of a facility location problem.

Multiperiod financial optimization is usually based on a stochastic model for the possible market situations. There is a rich literature about modeling and estimation of continuous-state financial processes, but little attention has been paid how to approximate such a process by a discrete-state scenario process and how to measure the pertaining approximation error.In this paper we show how a scenario tree may be constructed in an optimal manner on the basis of a simulation model of the underlying financial process by using a stochastic approximation technique. Consistency relations for the tree may also be taken into account.2. Observe the next trajectory ξ (s) .

The Value-at-Risk (V@R) is an important and widely used measure of the extent to which a given portfolio is subject to risk inherent in financial markets. In this paper, we present a method of calculating the portfolio which gives the smallest V@R among those, which yield at least some specified expected return. Using this approach, the complete mean-V@R efficient frontier may be calculated. The method is based on approximating the historic V@R by a smoothed V@R (SV@R) which filters out local irregularities. Moreover, we compare V@R as a risk measure to other well known measures of risk such as the Conditional Value-at-Risk (CV@R) and the standard deviation.It is shown that the resulting efficient frontiers are quite different. An investor, who wants to control his V@R should not look at portfolios lying on other than the V@R efficient frontier, although the calculation of this frontier is algorithmically more complex. We support these findings by presenting results of a large scale experiment with a representative selection of stock and bond indices from developed and emerging markets which involved the computation of many thousands of V@R-optimal portfolios.

No abstract