Search Results (18)

This paper investigates an infinite-horizon optimal consumption and investment problem for an agent who consumes two types of goods: necessities and luxuries. The agent derives utility from both goods but faces a ratcheting constraint on luxury consumption, which prohibits any decline in its level over time. This constraint captures the irreversible nature of high living standards or luxury habits often observed in real economies. We formulate the problem in a complete financial market with a risk-free asset and a risky stock and solve it analytically using the dual–martingale method. The dual problem is shown to reduce to a family of optimal stopping problems, from which we derive explicit closed-form solutions for the value function and optimal policies. Our results reveal that the ratcheting constraint generates asymmetric consumption dynamics: necessities adjust freely, whereas luxuries exhibit downward rigidity. As a consequence, the marginal propensity to consume necessities declines with wealth, while luxury consumption and portfolio risk exposure increase more sharply compared to the benchmark case without ratcheting. The model provides a continuous-time microfoundation for persistent high consumption levels and greater risk-taking among wealthy individuals. Full article

We study a finite-horizon optimal consumption and investment problem in a complete continuous-time market where consumption is restricted within fixed upper and lower bounds. Assuming constant relative risk aversion (CRRA) preferences, we employ the dual-martingale approach to reformulate the problem and derive closed-form integral representations for the dual value function and its derivatives. These results yield explicit feedback formulas for the optimal consumption, portfolio allocation, and wealth processes. We establish the duality theorem linking the primal and dual value functions and verify the regularity and convexity properties of the dual solution. Our results show that the upper and lower consumption bounds transform the linear Merton rule into a piecewise policy: consumption equals L when wealth is low, follows the unconstrained Merton ratio in the interior region, and is capped at H when wealth is high. Full article

Quadratic programming (QP) formulations are widely used in optimal investment portfolio selection, a central problem in financial decision-making. In practice, asset allocation decisions operate at two interconnected levels: the strategic level, which allocates the budget across major asset classes, and the tactical level, which distributes the allocation within each class to individual securities or instruments. This study evaluates the Frank–Wolfe (FW) algorithm as a computationally alternative to a QP formulation implemented in CVXPY and solved using OSQP (CVXPY–OSQP solver) for tactical investment portfolio optimization. By iteratively solving a linear approximation of the convex objective function, FW offers a distinct approach to portfolio construction. A comparative analysis was conducted using a tactical portfolio model with a small number of stock assets, assessing solution similarity, computational running time, and memory usage. The results demonstrate a clear trade-off between the two methods. While FW can produce portfolio weights closely matching those of the CVXPY–OSQP solver at lower and feasible target returns, its solutions differ at higher returns near the limits of the feasible set. However, FW consistently achieved shorter execution times and lower memory consumption. This study quantifies the trade-offs between accuracy and efficiency and identifies opportunities to improve FW’s accuracy through adaptive iteration strategies under more challenging optimization conditions. Full article

We study a finite-horizon optimal job-switching and portfolio allocation problem where an agent faces a mandatory retirement date. The agent can freely switch between two jobs with differing levels of income and leisure. The financial market consists of a risk-free asset and a risky asset, with the agent making dynamic consumption, investment, and job-switching decisions to maximize lifetime utility. The utility function follows a Cobb–Douglas form, incorporating both consumption and leisure preferences. Using a dual-martingale approach, we derive the optimal policies and establish a verification theorem confirming their optimality. Our results provide insights into the trade-offs between labor income and leisure over a finite career horizon and their implications for retirement planning and investment behavior. Full article

From the perspective of biogas plant (BGP) operators, it is highly challenging to make a profitable decision on optimal biomethane production and allocation across interconnected markets. The aim of this study is to analyze the dynamics of biomethane markets, develop the gas allocation portfolio (GAP) for BGPs, investigate the impact of GHG quota price on the market dynamics and substrate mix consumption, and evaluate the profitability of the biomethane market system under various demand-based scenarios. A two-step optimization approach based on linear programming is adopted. Firstly, the optimized substrate mix and corresponding GAP are determined for all BGPs. Secondly, by leveraging the options flexibility created by the interconnected nature of biomethane markets, the BGPs’ GAP is further developed. Through an in-depth sensitivity analysis, the effects of GHG quota price variations on the market dynamics are assessed. The results indicate that integrated production, obtained by implementing the improved GAP across all BGPs, maximizes the profitability of the system. At higher quota prices, the consumption of manure, residuals, and grass is encouraged, while the use of energy crops declines. Furthermore, higher quota prices lead to a substantial increase in biomethane price in the EEG market, highlighting the need for further governmental support for biomethane CHP units. The anticipated competition between hydrogen and biomethane to achieve a greater share in the heating sector could pose risks to long-term investments in biomethane. The system achieves its highest profitability, a total contribution margin of EUR 2254.8 million, under the Transport Biofuels Expansion scenario. Generally, policies and regulations that raise the quota price (e.g., the 36. BImSchV) or promote biomethane demand in the heating sector (e.g., the GEG) can provide both economic and ecological benefits to the system. Full article

For the net-zero emission goal by 2050, the government of Taiwan has mandated large electricity consumers to utilize 10% green electricity to mitigate carbon emissions. Major enterprises face challenges in selecting appropriate green power options and integrating the benefits of carbon reduction into corporate governance decision-making. This study aims to optimize the combination of various green power options through a system dynamics approach, incorporating existing power purchase conditions and electricity consumption data from enterprises. In addition, by utilizing financial estimations with the monetization of environmental benefits, we constructed a more complete evaluation model for enterprises transitioning to green power. The results indicate low investment returns in various green energy portfolios. However, if power storage equipment is utilized to participate in auxiliary services, the investment return of green energy can be significantly enhanced. This evaluation model is also available online for business professionals across various sectors to explore and reference. Full article

We study an optimal consumption, leisure, and investment problem over a finite horizon in a continuous-time financial market with partial borrowing constraints. The agent derives utility from consumption and leisure, with preferences represented by a Cobb–Douglas utility function. The agent allocates time between work and leisure, earning wage income based on working hours. A key feature of our model is a partial borrowing constraint that limits the agent’s debt capacity to a fraction of the present value of their maximum future labor income. We employ the dual-martingale approach to derive the optimal consumption, leisure, and investment strategies. The problem reduces to solving a variational inequality with a free boundary, which we analyze using analytical and numerical methods. We provide an integral equation representation of the free boundary and solve it numerically via a recursive integration method. Our results highlight the impact of the borrowing constraint on the agent’s optimal decisions and the interplay between labor supply, consumption, and portfolio choice. Full article

Against the backdrop of global climate change and sustainable development, carbon emissions within transnational closed-loop supply chains have become a critical area of research. This paper utilizes a Stackelberg game model to analyze the relationship between a single export manufacturer and an import retailer. The study investigates the optimal solutions of the supply chain model—wholesale price, retail price, sales volume, and profit—across three consumer preference scenarios: no obvious preference, pure green preference, and pure new preference. Furthermore, this paper examines the impact of carbon emissions per unit of product on supply chain decision-making under two scenarios: with and without carbon trading. Carbon trading, which significantly increases unit costs, exerts a profound influence on the strategic decisions of both manufacturers and retailers. In addition, this paper incorporates carbon tariffs and taxes into its analysis, providing a theoretical foundation for governments and policymakers to promote sustainable production and consumption practices. The validity of the model is confirmed through numerical simulations, which reveal that under pure green and pure new preference scenarios, original equipment manufacturers (OEMs) are more inclined to invest in emissions reduction to minimize tariff costs. In contrast, under no obvious preference scenarios, OEMs are more likely to adjust product portfolios to evade carbon tariffs. This research advances the understanding of low-carbon production strategies in transnational supply chains, offering both theoretical insights and practical guidance for balancing economic and environmental objectives. Full article

Liquefied natural gas (LNG), recognized as the fossil fuel with the lowest carbon emission intensity, is a crucial transitional energy source in the global shift towards low-carbon energy. As the natural gas industry undergoes rapid expansion, the complexity of investment business models has increased significantly. Optimizing the combination of various segments within the value chain has become standard practice, making it essential to control risks and enhance economic benefits in these multifaceted scenarios. This paper introduces an integrated economic model encompassing upstream, liquefaction, shipping, regasification, and consumption, suitable for both upstream and downstream integration. The model offers a comprehensive analysis of the primary business models and key factors across each segment of the value chain. By constructing a robust economic evaluation framework, the study aims to provide a holistic approach to understanding the economic feasibility of LNG projects. Two detailed case studies are conducted to demonstrate the application and effectiveness of the proposed model, highlighting its capability to guide investment decisions, support risk management, and optimize asset portfolios. The integrated economic model developed in this study serves as a valuable tool for stakeholders in the LNG industry. It not only facilitates informed investment decision-making but also enhances the strategic management of risks and resources. By leveraging this model, investors and managers can better navigate the complexities of the LNG business, ensuring sustainable and economically viable operations. Full article

This paper studies optimal consumption and investment strategies with lifetime uncertainty to design a smooth pension product. In a simplified Black–Scholes market, we investigate three strategies for consumption and investment: the classical strategy, the habit strategy, and the hybrid strategy. Incorporating additive habit formation in preferences leads to a request for less consumption volatility. Studying the consumption dynamics, it turns out that the hybrid strategy complies with the same preferences as the habit strategy. In our design of a smooth pension product, we are highly inspired by the consumption structure under the hybrid strategy and let consumption be specified as a time-dependent weighted average of last year’s consumption level and a standard market rate life annuity. We give two approaches for the investment portfolio. The numerical examples show that consumption under these approaches is less volatile than consumption under the classical strategy. Full article

Business parks account for 30% of China’s total carbon emissions. Exploring emissions reduction approaches for business parks is crucial to achieve a net-zero emissions target, as well as for achieving a representative example for all types of emissions entities. Business parks mainly adopt two types of emissions reduction approaches: energy-saving renovations and purchasing carbon reduction products. However, there are limited studies focusing on the optimal combinations of the two approaches for reaching net-zero emissions and evaluating the cost effectiveness. To find a feasible and quantified way to build net-zero business park, a comprehensive path decision model is proposed. The problem is broken down into two parts: the optimal carbon reduction portfolio and the optimal electricity saving were researched. For the optimal product portfolio, the Markowitz theory is employed to balance the risk of carbon reduction products with the expected cost. In the part of optimal electricity saving, considering a ten-year life cycle, the total cost includes renovation investment, carbon reduction products cost, and cost saving of electricity consumption reduction. Based on the energy consumption, technical, and price data, the combination of energy-saving renovations and carbon reduction products is optimized. The model suggests a business park can save 24% of energy consumption through renovation investment and purchase CCER as 66% of the carbon reduction product portfolio. Taking only purchasing carbon reduction products as a benchmark to assess economic efficiency, implementing an optimized level of energy-saving renovation is found to save 16% of the comprehensive cost for the life cycle required to achieve zero carbon emissions. This model provides a new comprehensive optimization idea that will help future parks make decisions to achieve zero-carbon emission targets. Full article

This manuscript derives optimal consumption and investment strategies for risk-averse investors under the 4/2 stochastic volatility class of models. We work under an expected utility (EUT) framework and consider a Constant Relative Risk Aversion (CRRA) investor, who may also be ambiguity-averse. The corresponding Hamilton–Jacobi–Bellman (HJB) and HJB–Isaacs (HJBI) equations are solved in closed-form for a subset of the parametric space and under some restrictions on the portfolio setting, for complete markets. Conditions for proper changes of measure and well-defined solutions are provided. These are the first analytical solutions for the 4/2 stochastic volatility model and the embedded 3/2 model for the type of excess returns established in the literature. We numerically illustrate the differences between the 4/2 model and the embedded cases of the 1/2 model (Heston) as well as the 3/2 model under the same data, and for two main cases: risk-averse investor in a complete market with consumption, and ambiguity-averse investor in a complete market with no consumption. In general, the 4/2 and 1/2 models recommend similar levels of consumption and exposure, while the 3/2 leads to significantly different recommendations. Full article

Saving and investment behaviour is crucial for all individuals to guarantee their welfare during work-life and retirement. We introduce a deep reinforcement learning model in which agents learn optimal portfolio allocation and saving strategies suitable for their heterogeneous profiles. The environment is calibrated with occupation- and age-dependent income dynamics. The research focuses on heterogeneous income trajectories dependent on agents’ profiles and incorporates the parameterisation of agents’ behaviours. The model provides a new flexible methodology to estimate lifetime consumption and investment choices for individuals with heterogeneous profiles. Full article

We investigate a portfolio selection problem involving an agent’s realistic housing service choice, where the agent not only has to choose the size of house to live in, but also has to select between renting and purchasing a house. Adopting a dynamic programming approach, we derive a closed-form solution to obtain the optimal policies for the consumption, investment, housing service, and purchasing time for a house. We also present various numerical demonstrations showing the impacts of parameters in the financial and housing markets and the agent’s preference, which visually show the economic implications of our model. Our model makes a significant contribution because it is a pioneering model for the optimal time to purchase a house, which has not been investigated in depth in existing mathematical portfolio optimization models. Full article

In the present paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting, a context that gives rise to time-inconsistency of the decision-maker. We consider equilibrium policies within the class of open-loop controls that are characterized, in our context, by means of a variational method which leads to a stochastic system that consists of a flow of forward-backward stochastic differential equations and an equilibrium condition. An explicit representation of the equilibrium policies is provided for the special cases of power, logarithmic and exponential utility functions. Full article