Dynamic Portfolio Optimization under Regime-Based Firm Strength

This thesis consists of three essays in financial economics, more precisely in the field of asset pricing and optimal portfolio choice. The first essay studies the asset pricing implications of heterogeneity in preferences coupled with long run risk in a dynamic general equilibrium pure exchange economy. It is concerned with the understanding of how risk sharing among different types of agents affects the assets returns moments in equilibrium and moreover, how these agents reacts dynamically to the long run risk that they perceive. The second and third essay approach the question of optimal portfolio with stochastic opportunity sets. The second essay proposes an approximation methodology for deriving approximate closed form solutions of dynamic optimal portfolio allocation problems. The third essay examines the optimal consumption, portfolio rule and life insurance purchase problem of a wage earner having uncertain lifetime when the market price of risk follows a mean-reverting stochastic process.

This study focuses on a two-stage hybrid framework for dynamic portfolio optimization. While existing two-stage approaches often rely mainly on price data, symmetric downside measures, or static allocation, they provide limited insight into fundamental efficiency and how assets behave during severe market downturns. In the first stage, Data Envelopment Analysis (DEA) is used to pre-select efficient stocks based on fundamental financial indicators. In the second stage, several risk-based allocation strategies are applied to the selected assets, including mean-standard deviation, semi-deviation, conditional value at risk, maximum Sharpe ratio, and a proposed mean-asymmetric downside risk model. This proposed model introduces an exponential penalty function to emphasize larger losses and better capture downside risk during market downturns. Portfolio performance is evaluated using a rolling-window approach with weekly rebalancing over a 65-week out-of-sample period. The DEA-based selection effectively reduced the investment universe from 36 to 9 efficient stocks. Empirical results show that the simple DEA+1/N portfolio outperformed the SET50 benchmark, and the proposed DEA+mAsymRisk delivered higher returns with lower downside risk compared to alternative strategies. These findings highlight that combining fundamental screening with downside-sensitive allocation strengthens portfolio robustness and offers practical value for dynamic risk management in financial markets.

The paper studies connections between arbitrage and utility maximization in a discrete-time financial market. The market is incomplete. Thus one has several choices of equivalent martingale measures to price contingent claims. Davis determines a unique price for a contingent claim which is based on an optimal dynamic portfolio by use of a `marginal rate of substitution' argument. Here conditions will be given such that this price is determined by a martingale measure and thus by a consistent price system. The underlying utility function U is defined on the positive half-line. Then dynamic portfolios are admissible if the terminal wealth is positive. In case of the logarithmic utility function, the optimal dynamic portfolio is the numeraire portfolio.

The paper studies connections between risk aversion and martingale measures in a discrete‐time incomplete financial market. An investor is considered whose attitude toward risk is specified in terms of the index b of constant proportional risk aversion. Then dynamic portfolios are admissible if the terminal wealth is positive. It is assumed that the return (risk) processes are bounded. Sufficient (and nearly necessary) conditions are given for the existence of an optimal dynamic portfolio which chooses portfolios from the interior of the set of admissible portfolios. This property leads to an equivalent martingale measure defined through the optimal dynamic portfolio and the index 0 < b≤ 1. Moreover, the option pricing formula of Davis is given by this martingale measure. In the case of b= 1; that is, in the case of the log‐utility, the optimal dynamic portfolio defines the numéraire portfolio.

In this paper, we consider the problem of an optimal pension fund portfolio given the heterogeneous risk preferences of pension fund participants. The relative risk aversion of a pension fund tends to be a decreasing function of the level of aggregate wealth. We find that the dynamic optimal portfolio is simply characterized as the weighted sum of the optimal portfolio for each participant. Our model helps successfully establish the microfoundation of asset liability management models. A numerical example using recent Japanese data indicates the significant total welfare losses of adopting a suboptimal portfolio strategy and an inefficient risk‐sharing rule.

In this paper, we develop a three-stage stochastic network-based optimization model for the provision of 5G services with Unmanned Aerial Vehicles (UAVs) in the disaster management phases of: preparedness, response and recover/reconstruction. Users or devices on the ground request services of a fleet of controller UAVs in flight and the requested services are executed by a fleet of UAVs organized as a Flying Ad-Hoc Network and interconnected via 5G technology. A disaster scenario can create difficulties for the provision of services by service providers. For this reason, in the first stage, service providers make predictions about possible scenarios in the second stage. Therefore, the first stage represents the preparedness phase, the second stage represents the response phase, followed by the recovery/reconstruction phase, represented by the third stage. In each of the three stages, service providers seek to maximize the amount of services to be performed, assigning each service a priority. They also aim to, simultaneously, minimize the total management costs of requests, the transmission and execution costs of services, the costs to increase the resources of the pre-existing network and, if need be, to reduce them in the recovery/reconstruction phase. For the proposed multi-stage stochastic optimization model, we provide variational formulations for which we investigate the existence and uniqueness of the solution. Finally, a detailed numerical example is solved in order underline some of the key aspects of the model. This paper adds to the literature on the rigorous mathematical modeling of advanced technologies for disaster management.

A probability constrained multi-objective optimization model for CCHP system operation decision support

We investigate a multiperiod, stochastic portfolio optimization model for diversified funds choices associated with traditional 401K or 403B plans. This optimization model minimizes the L1‐norm for negative return rate risk (the downside mean absolute deviation) while examining parameters that maintain model feasibility. Important components of the model are the incorporation of appropriate time‐series components and evaluation of scenarios based on investor outlook. A case study experimentation of the model on five potential investment funds using historical data from 2003 to 2013 was conducted, and parameter constraints for diversification and minimum acceptable return rates were manipulated to produce contour plots. The maximum geometric rate of return investment strategy provided by the optimization would have resulted in a 9.7% geometric return rate in 2014 as compared with a 5.0% for a uniform distribution of investment funds across choices.

Realized Covariance Estimation in Dynamic Portfolio Optimization

Portfolio optimisation is an important issue in the field of investment/financial decision-making and has received considerable attention from both researchers and practitioners. However, besides portfolio optimisation, a complete investment procedure should also include the selection of profitable investment targets and determine the optimal timing for buying/selling the investment targets. In this study, an integrated procedure using data envelopment analysis (DEA), artificial bee colony (ABC) and genetic programming (GP) is proposed to resolve a portfolio optimisation problem. The proposed procedure is evaluated through a case study on investing in stocks in the semiconductor sub-section of the Taiwan stock market for 4 years. The potential average 6-month return on investment of 9.31% from 1 November 2007 to 31 October 2011 indicates that the proposed procedure can be considered a feasible and effective tool for making outstanding investment plans, and thus making profits in the Taiwan stock market. Moreover, it is a strategy that can help investors to make profits even when the overall stock market suffers a loss.

Recently, different methods have been proposed for portfolio optimization and decision making on investment issues. This article aims to present a new method for portfolio formation based on Data Envelopment Analysis (DEA) and Entropy function. This new portfolio optimization method applies DEA in association with a model resulting from the insertion of the Entropy function directly into the optimization procedure. First, the DEA model was applied to perform a pre-selection of the assets. Then, assets given as efficient were submitted to the proposed model, resulting from the insertion of the Entropy function into the simplified Sharpe’s portfolio optimization model. As a result, an improved asset participation was provided in the portfolio. In the DEA model, several variables were evaluated and a low value of beta was achieved, guaranteeing greater robustness to the portfolio. Entropy function has provided not only greater diversity but also more feasible asset allocation. Additionally, the proposed method has obtained a better portfolio performance, measured by the Sharpe Ratio, in relation to the comparative methods.

Deep reinforcement learning (DRL) has been extensively used to address portfolio optimization problems. DRL agents acquire knowledge and make decisions through unsupervised interactions with their environment without requiring explicit knowledge of the joint dynamics of portfolio assets. Among these DRL algorithms, the combination of actor-critic algorithms and deep function approximators is the most widely used DRL algorithm. Here, we find that training the DRL agent using the actor-critic algorithm and deep function approximators may lead to scenarios where the improvement in the DRL agent's risk-adjusted profitability is insignificant. We argue that such situations primarily arise from the following two problems: sparsity in positive reward and the curse of dimensionality. These limitations prevent DRL agents from comprehensively learning asset price change patterns in the training environment. As a result, the DRL agents cannot effectively explore the dynamic portfolio optimization policy to improve the risk-adjusted profitability in the training process. To address these problems, we propose a novel multi-agent learning system based on the hierarchical deep reinforcement learning (HDRL) algorithmic framework in this research. Under this framework, the agents work together as a learning system for portfolio optimization. Specifically, by designing an auxiliary agent that works together with the executive agent for optimal policy exploration, the learning system can focus on exploring the policy with higher risk-adjusted return in the action space with positive return and low variance. The performance of the proposed learning system is evaluated using a portfolio of 29 stocks from the Dow Jones index in four different experiments. In the training process, the objective functions of the actor and critic both ultimately achieve stable convergence in the training process. The risk-adjusted profitability of our learning system in the training environment is significantly improved. Hence, we prove that the policies executed by our learning system in out-sample experiments originate from the DRL agents' comprehensive learning of asset price change patterns in the training environment. Furthermore, we find that adopting the auxiliary agent and HDRL training algorithm can efficiently overcome the issue of the curse of dimensionality and improve the training efficiency in the positive reward sparse environment. In each back-test experiment, the proposed learning system is compared to sixteen traditional strategies and ten strategies based on machine learning algorithms in the performance of profitability and risk control ability. The empirical results in the four evaluation experiments demonstrate the efficacy of our learning system, which outperforms all other strategies by at least 8.2% in terms of Sharpe ratio, Sorino ratio, and Calmar ratio. This indicates that the policies learned in the training environment can exhibit excellent generalization ability in the back-testing experiments.

Contributors

This paper determines the optimal bidding strategy of an electric vehicle (EV) aggregator participating in day-ahead energy and regulation markets using stochastic optimization. Key sources of uncertainty affecting the bidding strategy are identified and incorporated in the stochastic optimization model. The aggregator portfolio optimization model should include inevitable deviations between day-ahead cleared bids and actual real-time energy purchases as well as uncertainty for the energy content of regulation signals in order to ensure profit maximization and reliable reserve provision. Energy deviations are characterized as “uninstructed” or “instructed” depending on whether or not the responsibility resides with the aggregator. Price deviations and statistical characteristics of regulation signals are also investigated. Finally, a new battery model is proposed for better approximation of the battery charging characteristic. Test results with an EV aggregator representing one thousand EVs are presented and discussed.

We study the optimal dynamic portfolio exposure to predictable default risk, taking inspiration from the search for yield by means of defaultable assets observed before the 2007–2008 crisis and in its aftermath. Under no arbitrage, default risk is compensated by an ‘yield pickup’ that can strongly attract aggressive investors via an investment-horizon effect in their optimal non-myopic portfolios. We show it by stating the optimal dynamic portfolio problem of Kim and Omberg (Rev Financ Stud 9:141–161, 1996) for a defaultable risky asset and by rigorously proving the existence of nirvana-type solutions. We achieve such a contribution to the portfolio optimization literature by means of a careful, closed-form-yielding adaptation to our defaultable asset setting of the general convex duality approach of Kramkov and Schachermayer (Ann Appl Probab 9(3):904–950, 1999; Ann Appl Probab 13(4):1504–1516, 2003).