Optimal investment strategies for pension funds with regulation-conform dynamic pension payment management in the absence of guarantees

In this article we consider the post-retirement phase optimization problem for a specific pension product in Germany that comes without guarantees. The continuous-time optimization problem is defined consisting of two specialties: first, we have a product-specific pension adjustment mechanism based on a certain capital coverage ratio which stipulates compulsory pension adjustments if the pension fund is underfunded or significantly overfunded. Second, due to the retiree’s fear of and aversion against pension reductions, we introduce a total wealth distribution to an investment portfolio and a buffer portfolio to lower the probability of future potential pension shortenings. The target functional in the optimization, that is to be maximized, is the client’s expected accumulated utility from the stochastic future pension cash flows. The optimization outcome is the optimal investment strategy in the proposed model. Due to the inherent complexity of the continuous-time framework, the discrete-time version of the optimization problem is considered and solved via the Bellman principle. In addition, for computational reasons, a policy function iteration algorithm is introduced to find a stationary solution to the problem in a computationally efficient and elegant fashion. A numerical case study on optimization and simulation completes the work with highlighting the benefits of the proposed model.

Time Consistency of the Mean-Risk Problem

When dealing with dynamic optimization problems, time consistency is a desirable property as it allows one to solve the problem efficiently through a backward recursion. The mean-risk problem is known to be time inconsistent when considered in its scalarized form. However, when left in its original bi-objective form, it turns out to satisfy a more general time consistency property that seems better suited to a vector optimization problem. In “Time Consistency of the Mean-Risk Problem,” Kováĉova and Rudloff introduce a set-valued version of the famous Bellman principle and show that the bi-objective mean-risk problem does satisfy it. Then, the upper image, a set that contains the efficient frontier on its boundary, recurses backward in time. Kováĉova and Rudloff present conditions under which this recursion can be exploited directly to compute a solution in the spirit of dynamic programming. This opens the door for a new branch in mathematics: dynamic multivariate programming.

Dynamic programming and feedback analysis of the two dimensional tidal dynamics system

In this work, we consider the controlled two dimensional tidal dynamics equations in bounded domains. A distributed optimal control problem is formulated as the minimization of a suitable cost functional subject to the controlled 2D tidal dynamics equations. The existence of an optimal control is shown and the dynamic programming method for the optimal control of 2D tidal dynamics system is also described. We show that the feedback control can be obtained from the solution of an infinite dimensional Hamilton-Jacobi equation. The non-differentiability and lack of smoothness of the value function forced us to use the method of viscosity solutions to obtain a solution of the infinite dimensional Hamilton-Jacobi equation. The Bellman principle of optimality for the value function is also obtained. We show that a viscosity solution to the Hamilton-Jacobi equation can be used to derive the Pontryagin maximum principle, which give us the first order necessary conditions of optimality. Finally, we characterize the optimal control using the adjoint variable.

Determination of the Aspect-ratio Distribution of Gold Nanorods in a Colloidal Solution using UV-visible absorption spectroscopy

Knowledge of the distribution of the aspect ratios (ARs) in a chemically-synthesized colloidal solution of Gold Nano Rods (GNRs) is an important measure in determining the quality of synthesis, and consequently the performance of the GNRs generated for various applications. In this work, an algorithm has been developed based on the Bellman Principle of Optimality to readily determine the AR distribution of synthesized GNRs in colloidal solutions. This is achieved by theoretically fitting the longitudinal plasmon resonance of GNRs obtained by UV-visible spectroscopy. The AR distribution obtained from the use of the algorithm developed have shown good agreement with those theoretically generated one as well as with the previously reported results. After bench-marking, the algorithm has been applied to determine the mean and standard deviation of the AR distribution of two GNRs solutions synthesized and examined in this work. The comparison with experimentally derived results from the use of expensive Transmission Electron Microscopic images and Dynamic Light Scattering technique shows that the algorithm developed offers a fast and thus potentially cost-effective solution to determine the quality of the synthesized GNRs specifically needed for many potential applications for the advanced sensor systems.

Stochastic control for optimal power flow in islanded microgrid

<p>The problem of optimal power flow (OPF) in an islanded mircrogrid (MG) for hybrid power system is described. Clearly, it deals with a formulation of an analytical control model for OPF. The MG consists of wind turbine generator, photovoltaic generator, and diesel engine generator (DEG), and is in stochastic environment such as load change, wind power fluctuation, and sun irradiation power disturbance. In fact, the DEG fails and is repaired at random times so that the MG can significantly influence the power flow, and the power flow control faces the main difficulty that how to maintain the balance of power flow? The solution is that a DEG needs to be scheduled. The objective of the control problem is to find the DEG output power by minimizing the total cost of energy. Adopting the Rishel’s famework and using the Bellman principle, the optimality conditions obtained satisfy the Hamilton-Jacobi-Bellman equation. Finally, numerical examples and sensitivity analyses are included to illustrate the importance and effectiveness of the proposed model.</p>

Analysing Computer-Aided Manufacturing Systems and Optimising Work Sequence of Complex Shell Parts

A track record in application of multi-operational CNC machines shows that their using is efficient only in the case of a significant increase in productivity rate and a dramatically reduced time-to-market of new products. Manufacturing capabilities of multi-operational machines (MOM) have been most completely revealed when machining the complex shell parts. The more complicated is a design of the part and the more is the number of its surfaces to be machined and the number of tools desirable for its machining and positioning, the more efficient is the use. One way to improve the MOM machining rate is to reduce nonproductive machine time by decreasing the mutual overlap processing of the movable operating elements of the machine.To solve this problem, the computer-aided manufacturing (CAM) systems have been analysed. The analysis has shown that their capabilities are wide enough, however, these systems can calculate only the total execution time of the main manufacturing steps, but cannot calculate the nonproductive machine time and minimise it. This conclusion suggests that the task of optimizing the processing sequence is relevant. The research has shown that the problem can be solved by dynamic programming methods, one of which is the solution of the traveling salesman problem (the Bellman’s method). With a known processing schedule of all the elementary surfaces of the shell part, i.e. the known number of the manufacturing steps to be performed, each step is represented as a vertex of some graph, and technological links between the vertices of its edges. A mathematical model developed on the Bellman principle, which is adapted to the manufacturing tasks allows us to minimise mutual overlap processing time of the operating elements of the machine to perform all the steps in the optimal sequence. Based on the MOM model (1000VBF), the mathematical model has passed tests when machining the shell part with 26 manufacturing steps to reach up to 12% reduction of the nonproductive machine time, as a result of optimization.

NOVEL CONTROL APPROACH FOR OPTIMAL POWER FLOW IN HYBRID WIND-PHOTOVOLTAIC-DIESEL GENERATION SYSTEMS

The paper deals with a formulation of an analytical control model for optimal power flow in an islanded microgrid (MG). In an MG with load change, wind power fluctuation, sun irradiation power disturbance, that can significant influence the power flow, and hence the power flow control problem in real life system faces some new challenges. In order to maintain the balance of power flow, a diesel engine generator (DEG) needs to be scheduled. The objective of the control problem is to find the DEG output power by minimizing the total cost of energy. Using the Bellman principle, the optimality conditions obtained satisfy the Hamilton-Jacobi-Bellman equation, which depends on time and system states, and ultimately, leads to a feedback control or to the so called energy management to be implemented in a SCADA system

A COMPROMISE PROGRAMMING APPROACH TO MULTIOBJECTIVE MARKOV DECISION PROCESSES

A Markov decision process (MDP) is a general model for solving planning problems under uncertainty. It has been extended to multiobjective MDP to address multicriteria or multiagent problems in which the value of a decision must be evaluated according to several viewpoints, sometimes conflicting. Although most of the studies concentrate on the determination of the set of Pareto-optimal policies, we focus here on a more specialized problem that concerns the direct determination of policies achieving well-balanced tradeoffs. To this end, we introduce a reference point method based on the optimization of a weighted ordered weighted average (WOWA) of individual disachievements. We show that the resulting notion of optimal policy does not satisfy the Bellman principle and depends on the initial state. To overcome these difficulties, we propose a solution method based on a linear programming (LP) reformulation of the problem. Finally, we illustrate the feasibility of the proposed method on two types of planning problems under uncertainty arising in navigation of an autonomous agent and in inventory management.

Continuous-Time Optimal Portfolio Selection Strategy with Redemption Based on Stochastic Control

In this paper a continuous-time portfolio optimization decision with the redemption is made, a typical portfolio selection model is established by use of Bellman principle of optimality and HJB equation, we derive the optimal strategy and efficient frontier with general stochastic control technique. Its research methodologies can be applied in the practical work such as investment funds management and financial risk management to raise the scientificity of decisions. It is of great referential and inspirational value to provide solutions to practical problem in real investment process.