Regime-Switching Asset Allocation Using a Framework Combing a Jump Model and Model Predictive Control

This paper proposes a solution method for the discrete-time long-term dynamic portfolio optimization problem with state and asset allocation constraints. We use the ideas of Model Predictive Control (MPC) to solve the constrained stochastic control problem. MPC is a solution technique which was developed to solve constrained optimal control problems for deterministic control applications. MPC solves the optimal control problem with a receding horizon where a series of consecutive open-loop optimal control problems is solved. The aim of this paper is to develop an MPC approach to the problem of long-term portfolio optimization when the expected returns of the risky assets are modeled using a factor model based on stochastic Gaussian processes. We prove that MPC is a suboptimal control strategy for stochastic systems which uses the new information advantageously and thus is better than the pure optimal open-loop control. For the open-loop optimal control optimization, we derive the conditional portfolio distribution and the corresponding conditional portfolio mean and variance. The mean and the variance depend on future decision about the asset allocation. For the dynamic portfolio optimization problem, we consider constraints on the asset allocation as well as probabilistic constraints on the attainable values of the portfolio wealth. We discuss two different objectives, a classical mean–variance objective and the objective to maximize the probability of exceeding a predetermined value of the portfolio. The dynamic portfolio optimization problem is stated, and the solution via MPC is explained in detail. The results are then illustrated in a case study.

T HE analysis and control of various multiple-input multipleoutput (MIMO) systems have been well examined. In many of these systems, the activity and response of various outputs act over different time scales. One such example is an aircraft, where there exist specific inputs that drive certain outputs, allowing the aircraft to maneuver. These various outputs, however, tend to react over different periods because they are affected differently by each input and are often coupled. Controlling one output with an input at a specific rate to obtain a desirable responsemay not necessarily lead to a desirable response in another coupled output. Naturally, certain outputs may need to be managed at higher rates than others to maintain adequate levels of performance. Model predictive control (MPC) allows for an effective method of controlling MIMO systems where significant control coordination is needed to obtain a desired response. MPC is a form of control that uses a model of a particular system to obtain an optimized set of control actions to force the system to a desired reference condition. The aim of MPC is to determine, online, an optimal control sequence that minimizes the cost of reaching a reference condition within a given prediction horizon. A detailed summary of MPC and its associated benefits is presented in [1–3], ranging from stability and optimality issues of various MPC formulations to tuning parameter allocations and discretization effects. The primarymethod of regulating the nature of the output response is through the prediction horizon, which defines how far into the future the system is to “look ahead” from its current state to determine the optimal course of action in the future. The length of the prediction horizon itself has a significant effect on the closed-loop behavior. If the prediction horizon is short, then the optimized control sequence will be aggressive to minimize the error between the current state and the desired reference condition. If the prediction horizon is long, then the control inputs will be weaker, allowing for a long-term transition of the system toward the desired condition [2]. CertainMPCmethods [4,5] apply a single, global prediction horizon to the system,meaning that each output is being controlled equally, regardless of the output’s nature. From this perspective, it seems that using a prediction horizon that may be effective in controlling one output may be less than effective at controlling other outputs. Using a single global prediction horizon for MIMO processes may therefore seem impractical for MPC problems. A potential solution is to adopt a multiple prediction horizon strategy that allocates individual prediction horizons to the outputs that are being controlled. The prediction horizons for each tracked output can be tuned to operate within time scales specific to the output. The resulting controller will therefore be able to control that output within the limitations of the system, without greatly affecting the behavior of other outputs. The multiple prediction horizon case for a multivariable system has been considered in [6] with respect to continuous-time generalized prediction control and in [7] with respect to block model predictive control. Applications of variable prediction horizons to aMIMO system are also addressed in [8] relating specifically to spacecraft control. Recent advances in predictive control have led to its implementation onto aerospace systems [8–13] as well as unstable systems [14,15] and have provided more reliable methods of controlling models with nonlinear properties and constraints. The use of multiple prediction horizons becomes particularly useful when attempting to control systems with high degrees of cross coupling between outputs with multiple degrees of freedom. In such cases, having prediction horizons specific to certain tracked outputs may allow for a certain level of decoupling to be achieved, where the response of a particular output can be adjusted without greatly affecting the response of other tracked outputs. This Note develops a general multiple horizon predictive control scheme extending the Algebraic Model Predictive Control (AMPC) algorithm in its application to flight control discussed in [16]. This Note discusses briefly the structure of the AMPC algorithm for a global prediction horizon case, then extends the formulation to accommodate formultiple prediction horizons forMIMO systems. A brief discussion on the formulation of the optimal controller will be given for both constrained and unconstrained cases, followed by a detailed analysis of the application and effect of the multiple prediction horizon method on a highly coupled linear longitudinal aircraft model.

This paper presents a comprehensive review of electric induction motor (IM) drive systems. It conducts an evaluation and critical analysis of modern control techniques aimed at enhancing induction motors or IM drive performance, drawing insights from a systematic literature survey. This review paper introduces the mathematical and dynamic models of induction motors and control via two-level inverter drives. Furthermore, the paper offers an extensive review of model predictive control (MPC) for induction motors which is considered a vector control (VC) technique. The MPC are subdivision based on control parameters into two modes, model predictive current control (MPCC) and model predictive torque control (MPTC). The paper thoroughly examines each control technique, providing insights into mathematical control analysis, block diagrams, and operational mechanisms, as well as the advantages and disadvantages associated with the method. The model predictive control (MPC) stands out due to its distinct advantages, particularly in terms of simplicity, accuracy, and efficiency.

The allocation of pension funds has important theoretical value and practical significance, which improves the level of pension investment income, achieves the maintenance and appreciation of pension funds, and resolves the pension payment risk caused by population aging. The asset allocation of pension funds is a long-term asset allocation problem. Thus, the long-term risk and return of the assets need to be estimated. The covariance matrix is usually adopted to measure the risk of the assets, while calculating the long-term covariance matrix is extremely difficult. Direct calculations suffer from the insufficiency of historical data, and indirect calculations accumulate short-term covariance, which suffers from the dynamic changes of the covariance matrix. Since the returns of main assets are highly autocorrelated, the covariance matrix of main asset returns is time-varying with dramatic dynamic changes, and the errors of indirect calculation cannot be ignored. In this paper, we propose a novel Black–Litterman model with time-varying covariance (TVC-BL) for the optimal asset allocation of pension funds to address the time-varying nature of asset returns and risks. Firstly, the return on assets (ROA) and the covariance of ROA are modeled by VARMA and GARCH, respectively. Secondly, the time-varying covariance estimation of ROA is obtained by introducing an effective transformation of the covariance matrix from short-term to long-term. Finally, the asset allocation decision of pension funds is achieved by the TVC-BL model. The results indicate that the proposed TVC-BL pension asset allocation model outperforms the traditional BL model. When the risk aversion coefficient is 1, 1.5, and 3, the Sharp ratio of pension asset allocation through the TVC-BL pension asset allocation model is 13.0%, 10.5%, and 12.8% higher than that of the traditional BL model. It helps to improve the long-term investment returns of pension funds, realize the preservation and appreciation of pension funds, and resolve the pension payment risks caused by the aging of the population.

This paper investigates how investors who face both market risk (interest rate risk) and credit risk in addition to equity risk would optimally allocate their financial wealth in a dynamic, no arbitrage, continuous-time setup. I model credit risk through a defaultable zero-coupon bond and solve the stochastic differential equation of it under the recovery to market value scheme. I obtain a closed-form solution to this investment problem, which enables me to analyze the impact on investors' decisions of various risk parameters. One interesting insight of this paper is that a non-zero recovery rate of the credit-risky bond affects investors' decision in a fundamental way. This is manifested in a dividend-like adjustment term in the drift of the stochastic differential equation (SDE) of the defaultable zero-coupon bond's return process. The optimal asset allocation involves the separation effect and effect. As a result, the relation between myopic demands for bonds and market prices of risk becomes relatively complicated compared with that in the traditional setup. In addition, I show the cross-markets correlation is an important factor in the asset allocation decision. In particular, it affects investors' ability to hedge against or speculate on the stochastic risk premium of the defaultable bond. Numerical examples show that the inclusion of credit markets significantly enhances investors' welfare. I also find modeling interest rate as a stochastic process greatly reduces model risk, giving investors more realistic prospects in their investment decisions. Key Words: integration of market risk and credit risk, asset allocation, welfare analysis, corporate bond, model risk

Model predictive control techniques are characterized by a variable switching frequency which cause noise as well as large voltage and current ripple. In this paper a predictive control strategy with a fixed switching frequency for a single-phase active power filter, namely modulated model predictive control, is proposed. This technique produces modulated waveform at the output of the converter. The feasibility of this strategy is evaluated using simulation results to demonstrate the advantages of predictive control, such as fast dynamic response and the easy inclusion of nonlinearities. The constraints of the system are maintained but the performance of the system in terms of power quality is improved compared to the traditional model predictive control strategy.

The model predictive control method can be effective for converter control in distributed power generation but requires a large amount of computation, leading to a considerable time delay in the actuation. If the delay is not reflected, the system performance could get worse. This paper presents a two-step (horizon) prediction algorithm of model predictive control technique for grid-tied inverters used in wind turbine systems. The control objectives such as active and reactive power flow and switching loss reduction are reflected in the objective function of the controller. The proposed model predictive control strategy is verified numerically by using MATLAB/Simulink.

<div class="section abstract"><div class="htmlview paragraph">This paper presents the characteristics of more than 260 trim levels for over 50 production electric vehicle (EV) models on the market since 2014. Data analysis shows a clear trend of all-wheel-drive (AWD) powertrains being increasingly offered on the market from original equipment manufacturers (OEMs). The latest data from the U.S. Environmental Protection Agency (EPA) shows that AWD EVs have seen a nearly 4 times increase in production from 21 models in 2020 to 79 models in 2023. Meanwhile single axle front-wheel-drive (FWD) and rear-wheel-drive (RWD) drivetrains have seen small to moderate increases over the same period, going from 9 to 11 models and from 5 to 12 models, respectively. Further looking into AWD architectures demonstrates dual electric machine (EM) powertrains using different EM types on each axle remain a small portion of the dual-motor AWD category. However, these architectures have been shown to have energy savings of 1 % to 5 % over that of identical dual-motor permanent magnet (PM) machine or dual-motor induction machine (IM) architectures. Further work shows dual motor architectures with an IM powering the front axle and a PM machine powering the rear axle under mathematical optimization-based controls to be less energy consuming than the same architecture subjected to a rule-based energy management strategy (EMS). This leads to a review of electrified vehicle EMSs, with the two main methods of rule-based and optimization-based controls being presented. The pros and cons of each control method are stated with optimization-based methods showing the most benefit. The optimal control method of model predictive control (MPC) is then presented by covering its’ background, structure, variations, and mechanics. Finally, the use of MPC as a viable EMS for multi-motor EVs is reviewed with motor thermal regulation as part of the control objective.</div></div>

Reinforcement learning is a machine learning approach concerned with solving dynamic optimization problems in an almost model-free way by maximizing a reward function in state and action spaces. This property makes it an exciting area of research for financial problems. Asset allocation, where the goal is to obtain the weights of the assets that maximize the rewards in a given state of the market considering risk and transaction costs, is a problem easily framed using a reinforcement learning framework. So it is first a prediction problem for the vector of expected returns and covariance matrix and then an optimization problem for returns, risk, and market impact, usually a quadratic programming one. Investors and financial researchers have been working with approaches like mean-variance optimization, minimum variance, risk parity, and equally weighted and several methods to make expected returns and covariance matrices' predictions more robust and after use mean-variance like the Black Litterman model. This paper demonstrates the application of reinforcement learning to create a financial model-free solution to the asset allocation problem, learning to solve the problem using time series and deep neural networks. We demonstrate this on daily data for the top 24 stocks in the US equities universe with daily rebalancing. We use a deep reinforcement model on US stocks using different deep learning architectures. We use Long Short Term Memory networks, Convolutional Neural Networks, and Recurrent Neural Networks and compare them with more traditional portfolio management approaches like mean-variance, minimum variance, risk parity, and equally weighted. The Deep Reinforcement Learning approach shows better results than traditional approaches using a simple reward function and only being given the time series of stocks. In Finance, no training to test error generalization results come guaranteed. We can say that the modeling framework can deal with time series prediction and asset allocation, including transaction costs.

Preface. 1. INTRODUCTION. 1.1 The Private Banking Business. 1.2 Current Challenges in Private Banking. 1.3 Improving Service Quality with Behavioural Finance. 1.4 Conclusion0. 2. DECISION THEORY. 2.1 Introduction. 2.2 Mean-Variance Analysis. 2.3 Expected Utility Theory. 2.4 Prospect Theory. 2.5 Prospect Theory and the Optimal Asset Allocation. 2.6 A Critical View on Mean-Variance Theory. 2.7 A Critical View on Expected Utility Axioms. 2.8 Comparison of Expected Utility, Prospect Theory, and Mean Variance Analysis. 2.9 Conclusion. 3. BEHAVIOURAL BIASES. 3.1 Information Selection Biases. 3.2 Information-Processing Biases. 3.3 Decision Biases. 3.4 Decision Evaluation Biases. 3.5 Biases in Inter-Temporal Decisions. 3.6 Behavioural Biases and Speculative Bubbles. 3.7 Cultural Differences in the Behavioural Biases. 4. RISK PROFILING. 4.1 Dealing with Behavioural Biases. 4.2 The Risk Profiler and its Benefits. 4.3 Designing a Risk Profiler: Some General Considerations. 4.4 Implemented Risk Profilers: Case Study former Bank Leu. 4.5 A Risk Profiler Based on the Mean-Variance Analysis. 4.6 Integrating Behavioural Finance in the Risk Profiler. 4.7 Case Study: Comparing Risk Profiles. 4.8 Conclusion. 5. PRODUCT DESIGN. 5.1 Case Study 'Ladder Pop'. 5.2 Case Study 'DAX Sparbuch'. 5.3 Optimal Product Design. 5.4 Conclusion. 6. DYNAMIC ASSET ALLOCATION. 6.1 The Optimal Tactical Asset Allocation. 6.2 The Optimal Strategic Asset Allocation. 6.3 Conclusion. 7. LIFE CYCLE PLANNING. 7.1 Case Study: Widow Kassel. 7.2 Main Decisions over Time. 7.3 Consumption Smoothing. 7.4 The Life Cycle Hypothesis. 7.5 The Behavioural Life Cycle Hypothesis. 7.6 The Life Cycle Asset Allocation Problem. 7.7 The Life Cycle Asset Allocation of an Expected Utility Maximizer. 7.8 The Life Cycle Asset Allocation of a Behavioural Investor. 7.9 Life Cycle Funds. 7.10 Summary 207. 8. STRUCTURED WEALTH MANAGEMENT PROCESS. 8.1 The Benefits of a Structured Wealth Management Process. 8.2 Problems Implementing a Structured Wealth Management Process. 8.3 Impact of the New Process on Conflicts of Interests. 8.4 Learning by 'Cycling' Through the Process. 8.5 Case Study: Credit Suisse. 8.6 Mental Accounting in the Wealth Management Process. 8.7 Conclusions. 9. CONCLUSION AND OUTLOOK. 9.1 Recapitulation of the main achievements. 9.2 Outlook of further developments. References. List of Notation. List of Figures. List of Tables.

To accomplish an accurate and fast drive control, model predictive control (MPC) is considered as an effective control strategy nowadays. In MPC, the voltage vectors required for inverter control are evaluated considering the control objectives defined in terms of current or power or torque and flux. The optimal one is selected using an iterative prediction loop and applied in the next control interval. This form of MPC is simple in implementation and shows appreciable dynamic performance but the steady-state performance is compromised due to the limited availability of the number of voltage vectors, especially in the case of a two-level voltage source inverter. The present article explores the viability of the MPC approach for a new candidate such as a brushless doubly fed reluctance machine drive considering its secondary current as the control variable. Moreover, to tackle the steady-state inferiority issue, the duty-cycle control concept is inducted. In comparison to field-oriented control (FOC), the proposed scheme offers a straightforward solution for current control by replacing the inner current proportional-integral controllers and pulsewidth modulator with an optimization-based model predictive current controller. An extensive simulation study in MATLAB, vis-à-vis comparison with FOC scheme, and experimental validations justify the claims of the proposed work.

This paper compares two torque control methodologies, namely Field Oriented and Model Predictive ones, for monitoring Interior Permanent Magnet Motor (IPMM) over a wide speed range. IPMM magnetic saturation and cross coupling effects are taken into consideration, increasing significantly the precision of the developed controllers. Maximum Torque per Ampere (MTPA) and Field Weakening (FW) operating modes below and above the rated speed, respectively, are considered for an Electric Vehicle (EV) application. In the Field Oriented Control (FOC) case, this is achieved by implementing convenient Look-Up Tables (LUT) and PI controllers, while in the Model Predictive Control (MPC) case it is obtained via a particular cost function. Moreover, in the MPC case, an additional power loss tracking factor is introduced in the cost function, in order to minimize the total motor losses over the entire drive cycle. The proposed control techniques are evaluated under both steady state and dynamic conditions, illustrating the relative advantages of MPC in terms of robustness and dynamic behavior.

Purpose The purpose of this paper is to investigate whether asset allocation across various industries listed on the Ghana Stock Exchange (GSE) varies across different monetary policy states. Design/methodology/approach This paper adopts the Markov Chain technique to split monetary policy into three different states. The authors further adopt the Markowitz portfolio optimization technique to find the minimum variance and optimum portfolio for the industries listed on the GSE. Findings The finding reveals a dynamic asset allocation, which varies the industry’s weight mix across the various monetary policy states enhance excess returns compared to the static asset allocation. Specifically, the authors find risk-return trade-off among industries listed on the GSE. Financial and Food and Beverage industries portfolios record high returns relative to the Government of Ghana 91-day Treasury bill. The Food and Beverage portfolio is the only portfolio that records relatively high excess returns across all the monetary policy states. The authors also find that, during expansionary state (high monetary policy rates) of the monetary policy, investors are to allocate about 69 and 30 percent of their investment into food and beverages and financials, respectively. Corner solution is found in the transient state where 100 percent of wealth is allocated to financial to obtain the optimum portfolio. The optimum portfolio in the contraction state assigns 52 percent to financials and 42 percent to manufacturing. In summary, the result supports the dependence of investors’ asset allocation decisions on monetary policy. Practical implications Therefore, the authors propose an investment strategy which is dynamic and takes into consideration the monetary policy states rather than static asset allocation which maintains the same industry weight mix over the investment period. Social implications In sum, the authors interpret the result as support for the dependence of investors’ asset allocation decisions on monetary policy. In Ghana, an increase in the monetary policy appears to support industries listed on the equity market. The result also gives knowledge about investors’ asset allocation decisions on the GSE, which is practical balanced source of information for investors’ risk and return choices. For a prudent monetary policy framework, the monetary policy committee should monitor industries listed on the GSE. The result from the analysis has also an implication for investors, portfolio managers and fund managers to consider the state of the monetary policy in Ghana when making investment decisions. Originality/value The study differs from earlier research on asset allocation by breaking new grounds on two levels. First of all, based on the notion that different industries have different exposures to monetary policy states, the authors extend the portfolios by grouping the equities listed on the GSE into their industrial sectors. Second, the authors examine how investors’ optimal portfolio allocation may change depending on the state of monetary policy.

The main topic of this thesis is control of dynamic systems that are subject to stochastic disturbances and constraints on the input and the state. The main motivation for dealing with control of such systems is that there is no method available that adequately deals with this problem, despite the fact that stochastic, constrained systems are often encountered in real world problems. For example, in process industry the margins of physical quantities such as temperature, pressure, concentration, velocity and position can be expressed as amplitude constraints in a natural way. Such constraints are usually persistent in that suitable control actions need to be implemented that respect these constraints irrespective of the presence of uncontrolled disturbances that effect the system. Goals of the thesis are to 1. Formulate a mathematical problem for the synthesis of a controller that will achieve desired performance of the controlled system. More precisely, to minimize a performance measure that captures desired performance while respecting constraints in the face of stochastic disturbances. 2. Deduce verifiable conditions under which the problem formulated in 1. is solvable. 3. Formulate a solution concept for the problem in 1. that is based on the model predictive control technique. 4. Create feasible computational algorithms for the synthesis of controllers that solve control problems from 1. within the solution setup from 3. 5. Investigate convergence properties of the approximate solutions obtained by computational algorithms from 4. The main tool that is used in the thesis to solve the problem formulated in 1. is the model predictive control technique. Model predictive control has had a significant and widespread impact on industrial process control. When dealing with stochastic systems, however, application of the standard model predictive control algorithms results in a significant loss in the controlled system performance. Therefore, to deal with the problem 1. within the model predictive control framework, it was necessary to develop alternative model predictive control techniques. Contributions of the thesis are twofold. The first set of contributions is made with regard to the model predictive control of constrained, stochastic systems. In this thesis, we develop a novel approach to the model predictive control of such systems, that is based on the optimization in closed loop over the control horizon and stochastic sampling of the disturbance i.e. a randomized algorithm. The second set of contributions has been made in more general framework of the optimal control of stochastic systems that are subject to input and state constraints. We present a novel problem setup for control of such systems and give initial results that are concerned with solvability conditions for the posed optimization problem and the characterization of the optimal solution.

Most retirement withdrawal rate studies are either based on historical data or use a particular assumption about portfolio returns unique to the study in question. But planners may have their own capital market expectations for future returns from stocks, bonds, and other assets they deem suitable for their clients’ portfolios. These uniquely personal expectations may or may not bear resemblance to those used for making retirement withdrawal rate guidelines. The objective here is to provide a general framework for thinking about how to estimate sustainable withdrawal rates and appropriate asset allocations for clients based on one’s capital market expectations, as well as other inputs about the client including the planning horizon, tolerance for exhausting wealth, and personal concerns about holding riskier assets. The study also tests the sensitivity of various assumptions for the recommended withdrawal rates and asset allocations, and finds that these assumptions are very important. Another common feature of existing studies is to focus on an optimal asset allocation, which is expected either to minimize the probability of failure for a given withdrawal rate, or to maximize the withdrawal rate for a given probability of failure. Retirement withdrawal rate studies are known in this regard for lending support to stock allocations in excess of 50 percent. This study shows that usually there are a wide range of asset allocations which can be expected to perform nearly as well as the optimal allocation, and that lower stock allocations are indeed justifiable in many cases.