Chair: Georgios Aivaliotis, University of Leeds, United Kingdom
Investment Stochastic Optimal Energy Planning
Thuener Silva (email@example.com), Marcus Poggi (firstname.lastname@example.org), Bruno Flach (email@example.com)
This paper presents a new approach to solve the mid- and long-term stochastic reliability planning for power systems accounting for multiple dispatch scenarios and the simultaneous failure of grid elements. The problem is formulated so as to minimize the sum of investment and expected operational costs and incorporates the decision-dependent nature of the probability distribution of random failure events. The proposed solution scheme uses generation of cutting planes as a linearization technique and importance sampling to allow for the solution of large instances of the problem.
Keywords: Endogenous uncertainty, stochastic programming, energy Planning
Modeling multi-stage decision optimization problems
Ronald Hochreiter (firstname.lastname@example.org)
Multi-stage optimization under uncertainty is a valuable methodology for modeling long-term management problems. Although many optimization modeling language extensions as well as computational environments to handle multi-stage problems have been proposed, the acceptance of this technique is generally low, due to the inherent complexity. In this paper a simplification to annotate multi-stage stochastic programs is proposed - contrary to the common approach to create an extension on top of an existing optimization modeling language.
Keywords: Optimization under Uncertainty, Stochastic Programming, Modeling Languages
Investment strategies and compensation of a mean–variance optimizing fund manager
Georgios Aivaliotis (G.Aivaliotis@leeds.ac.uk), Jan Palczewski (J.Palczweski@leeds.ac.uk)
In this paper, we present theoretical and numerical results for the optimization of a mean–variance functional based on the terminal- time value or on the whole trajectory of the underlying process. An optimization problem of this form cannot be studied directly by employing dynamic programming methods. We reformulate it as a superposition of a static and a dynamic optimization problem, where the latter is feasible for dynamic programming methods. We characterize its value function as the unique continuous, polynomially growing, viscosity solution to an appropriate degenerate Hamilton–Jacobi–Bellman equation. Our reformulation of the mean–variance problem allows us to numerically calculate the value function and an optimal strategy for a pre-determined risk-aversion coefficient. We apply this theory to the delegated portfolio management problem: given a compensation contract, a mean–variance optimizing fund manager seeks a trading strategy that maximizes her (risk-adjusted) compensation. Our mathematical and numerical framework can accommodate optimization problems induced by complex (real-world) contracts. In particular, we are able to study the relatively unexplored relations between strategies pursued by managers remunerated according to schemes based on the terminal wealth and on the continuously monitored wealth. Surprisingly, terminal-wealth based schemes turn out to induce more prudent investment behavior and superior performance than the schemes that rely on the continuously monitored wealth. Previous literature shows, in a discrete-time setting, an advantage of frequent monitoring of portfolio value. Our continuous- time results contradict this finding.
Keywords: Mean-variance, Managerial compensation, Investment strategies