infonet-economy

A discretization scheme for a portfolio selection problem is discussed. The model is a benchmark relative, mean-variance optimization problem in continuous time. In order to make the model computationally tractable, it is discretized in time and space. This approximation scheme is designed in such a way that the optimal values of the approximate problems yield bounds on the optimal value of the original problem. The convergence of the bounds is discussed as the granularity of the discretization is increased. A threshold accepting algorithm that attempts to find the most accurate discretization among all discretizations of a given complexity is also proposed. Promising results of a numerical case study are provided.

The classical Markowitz approach to portfolio selection is compromised by two major shortcomings. First, there is considerable model risk with respect to the distribution of asset returns. Particularly, mean returns are notoriously difficult to estimate. Moreover, the Markowitz approach is static in that it does not account for the possibility of portfolio rebalancing within the investment horizon. We propose a robust dynamic portfolio optimization model to overcome both shortcomings. The model arises from an infinite-dimensional min-max framework. The objective is to minimize the worst-case portfolio variance over a family of dynamic investment strategies subject to a return target constraint. The worst-case variance is evaluated with respect to a set of conceivable return distributions. We develop a quantitative approach to approximate this intractable problem by a tractable one and report on numerical experiments.

In a dynamic investment situation, the right timing of portfolio revisions and adjustments is essential to sustain long-term growth. A high rebalancing frequency reduces the portfolio performance in the presence of transaction costs, whereas a low rebalancing frequency entails a static investment strategy that hardly reacts to changing market conditions. This article studies a family of portfolio problems in a Black-Scholes type economy which depend parametrically on the rebalancing frequency. As an objective criterion we use log-utility, which has strong theoretical appeal and represents a natural choice if the primary goal is long-term performance. We argue that continuous rebalancing only slightly outperforms discrete rebalancing if there are no transaction costs and if the rebalancing intervals are shorter than about one year. Our analysis also reveals that diversification has a dual effect on the mean and variance of the portfolio growth rate as well as on their sensitivities with respect to the rebalancing frequency.

Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vectors are inherently difficult to solve. In fact, scenario tree-based algorithms are unsuitable for problems with many stages, while dynamic programming-type techniques are unsuitable for problems with many state variables. This paper proposes a stage aggregation scheme for stochastic optimization problems in continuous time, thus having an extremely large (i.e., uncountable) number of decision stages. By perturbing the underlying data and information processes, we construct two approximate problems that provide bounds on the optimal value of the original problem. Moreover, we prove that the gap between the bounds converges to zero as the stage aggregation is refined. If massive aggregation of stages is possible without sacrificing too much accuracy, the aggregate approximate problems can be addressed by means of scenario tree-based methods. The suggested approach applies to problems that exhibit randomness in the objective and the constraints, while the constraint functions are required to be additively separable in the decision variables and random parameters.

This article describes a bounding approximation scheme for convex multistage stochastic programs (MSP) that constrain the conditional expectation of some decision-dependent random variables. Expected value constraints of this type are useful for modelling a decision maker's risk preferences, but they may also arise as artifacts of stage-aggregation. We develop two finite-dimensional approximate problems that provide bounds on the (infinite-dimensional) original problem, and we show that the gap between the bounds can be made smaller than any prescribed tolerance. Moreover, the solutions of the approximate MSPs give rise to a feasible policy for the original MSP, and this policy's optimality gap is shown to be smaller than the difference of the bounds. The considered problem class comprises models with integrated chance constraints and conditional value-at-risk constraints. No relatively complete recourse is assumed.

Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen negative events. In order to ensure computational tractability, continuous-state stochastic programs are usually discretized; and frequently, the curse of dimensionality dictates that decision stages must be aggregated. In this article we construct two discrete, stage-aggregated stochastic programs which provide upper and lower bounds on the optimal value of the original problem. The approximate problems involve finitely many decisions and constraints, thus principally allowing for numerical solution.

Electricity swing options are Bermudan-style path-dependent derivatives on electrical energy. We consider an electricity market driven by several exogenous risk factors and formulate the pricing problem for a class of swing option contracts with energy and power limits as well as ramping constraints. Efficient numerical solution of the arising multistage stochastic program requires aggregation of decision stages, discretization of the probability space, and reparameterization of the decision space. We report on numerical results and discuss analytically tractable limiting cases.

We examine the effects of CSR disclosure and CSR performance on firm value for the S&P 500 firms from 2011 to 2014 in this paper. We find that CSR disclosure is positively associated with firm value and that CSR disclosure dominates the effects of CSR performance on firm value. On average, the overall firm value increase for one index point of Bloomberg’s ESG Disclosure Score is $245 million, whereas the increase for one index point of the Asset4 ESG Performance Score is $93 million. Moreover, we find that the environmental and the governmental CSR performance scores are positively associated with firm value and that the social score is negatively associated. Our results suggest that CSR disclosure mediates CSR performance. Based on prior research, we argue that CSR disclosure is positively biased and too complex to be processed properly, so investors confuse CSR disclosure with CSR performance.