Optimal Investment Strategy Research Articles

Optimal investment strategies under the relative performance in jump-diffusion markets

AbstractWe work on a portfolio management problem for one agent and a large group of agents under relative performance concerns in jump-diffusion markets with the CRRA utility function. Herein, we define two wealth dynamics: the agent’s and the group’s wealth. We measure the performances of both the agent and the group with preferences linked to the group performance. Therefore, we have stochastic optimal control problems for both the representative agent and the group to determine what the group does and the agent’s optimal proportion in the portfolio relative to the group’s performance. Further, our framework assumes that the agent’s performance does not affect the group, while the group affects the agent’s utility. Moreover, we investigate special cases where all agents in the market are homogeneous in their risk aversion and relative performances. We explore the qualitative behavior of the agent and show some numerical results depending on her relative performance consideration and risk tolerance degree.

Probability weighting and equity premium prediction: Investing with optimism

AbstractEmpirically motivated theoretical models of probability weighting which overweight tail events are finding many applications in finance. However, probability weighting has not yet been applied to equity premium prediction or to constructing optimal market timing investment strategies. We show that a measure of market optimism from a representative agent asset pricing model with probability weighting can be used to construct optimal dynamic investment strategies that outperform the buy‐and‐hold strategy and strategies generated by 17 leading equity premium predictors. We further show that this theory‐based measure of market optimism predicts the equity premium and market Sharpe ratio in‐sample and out‐of‐sample. The predictability is not subsumed by disaster probabilities, market sentiment, or market skewness. Our results indicate that our theory‐based measure provides a distinct channel for predicting aggregate stock returns.

Forecasting stock index closing points using ARIMA-GARCH with a rolling data window

This research develops and examines the efficacy of a hybrid ARIMA-GARCH model, augmented by a rolling data window approach, to enhance the accuracy of stock index prediction, specifically focusing on the NEPSE index. Accurate predictions of stock indices are of paramount importance to investors, analysts and policy makers to navigate and circumvent the market uncertainties. The AutoRegressive Integrated Moving Average (ARIMA) model captures linear trends and temporal dependencies in time series data, while the General AutoRegressive Conditional Heteroskedasticity (GARCH) model addresses volatility clustering—ubiquitous character of financial time series—thereby providing a comprehensive framework for prediction. Utilizing a dataset comprised of daily closing points of NEPSE index approximately three years and nine months, the study identifies the ARIMA (5,1,0)-GARCH (1,1) model as optimal fit, upon integrating 180-day rolling data window. This model achieved a Mean Percentage Error of -0.0058% and a correlation of 0.995, which is indicative of superior fit to the underlying time series data. These findings underscore the hybrid model’s capacity to adaptively respond to dynamic market conditions and acclimatize prediction parallel to most recent market trends and volatility. This research is useful for optimizing investment strategies for those invested in Nepalese stocks. Also, this research lays a foundational framework for future investigations into application of this advanced forecasting method in other emerging markets, financial instruments and indices.

A Global-in-Time Neural Network Approach to Dynamic Portfolio Optimization

ABSTRACT We discuss a neural network approach, which does not rely on dynamic programming techniques, to solve dynamic portfolio optimization problems subject to multiple investment constraints. The approach allows for objectives of a very general form encompassing both time-consistent and time-inconsistent objectives, as well as objectives requiring multi-level optimization. The number of parameters of the neural network remains independent of the number of portfolio rebalancing events. Compared to reinforcement learning, this technique avoids the computation of high-dimensional conditional expectations. The approach remains practical when considering large numbers of underlying assets, long investment time horizons or very frequent rebalancing events. We prove convergence of the numerical solution to the theoretical optimal solution of a large class of problems under fairly general conditions, and present ground truth analyses for a number of popular formulations, including mean-variance, mean-semi-variance, and mean-conditional value-at-risk problems. Numerical experiments show that if the investment objective functional is separable in the sense of dynamic programming, the correct time-consistent optimal investment strategy is recovered, otherwise we obtain the correct pre-commitment (time-inconsistent) investment strategy. This method is agnostic as to the underlying data generating assumptions, and results are illustrated using (i) parametric models for underlying asset returns, (ii) stationary block bootstrap resampling of empirical returns, and (iii) generative adversarial network (GAN)-generated synthetic asset returns.

Pension funds with longevity risk: An optimal portfolio insurance approach

We present a unified framework designed to provide an optimal investment strategy for members of a defined contribution pension plan. Our model guarantees a minimum retirement savings level, expressed as a target annuity, by assuming uncertainty in interest rates, labor income, and mortality during the accumulation phase. To protect the accumulated retirement capital against both investment and longevity risks, the present value of the guaranteed lifetime annuity is regarded as the baseline wealth to hold upon reaching the retirement date, while a purpose-oriented proportion portfolio strategy is employed to invest the residual wealth. By applying standard dynamic programming techniques, we determine a closed-form solution to the stochastic control problem with the objective of maximizing the expected utility of the final surplus, defined as the difference between the accumulated wealth and the target annuity value. The theoretical findings are bolstered by a comprehensive numerical analysis designed to assess the impact of longevity on investment policies, highlighting the suitability of our proposal for managing defined contribution schemes.

Optimizing Taxi-Pooling Operations to Enhance Efficiency and Revenue: A Queuing Model Approach

This study investigates the optimization of taxi-pooling operations using the M/M/1/m queuing model, aiming to enhance efficiency and revenue for taxi service platforms. Traditional taxi operations face challenges during peak periods, including inefficiency and increased operational costs. Taxi-pooling, by accommodating multiple passengers with similar travel demands, offers a solution that reduces travel costs, operational expenses, and urban congestion. The study develops an optimization model to balance operational costs and passenger waiting times, identifying the utilization rate of taxis as a critical factor in platform revenue. By modeling the taxi-pooling service as a queuing system, we derive mathematical expressions for passenger waiting times and platform revenue under varying conditions. Our findings highlight the importance of optimal vehicle investment strategies and pricing decisions to maximize revenue. The study provides theoretical support for improving taxi-pooling platforms’ efficiency and competitiveness, contributing to better urban transportation solutions.

Comparative Analysis of Financial Optimization Scenarios for PV and Battery Storage Integration at Heraklion Port

The rapid expansion of renewable energy, driven by reduced installation costs, technological advancements, and political support, necessitates efficient integration strategies. This study presents a comparative analysis of financial optimization scenarios for the integration of photovoltaic (PV) systems and battery storage at Heraklion Port. By evaluating multiple strategies, the research addresses the economic viability, cost-benefit ratios, and payback periods of different configurations. This analysis considers the broader context of increasing pressure on electricity grids and the need for sustainable solutions to manage dispersed renewable production and energy offsetting. The findings aim to provide insights into optimal investment strategies that balance financial performance with energy efficiency, thereby mitigating costs passed on to consumers and supporting the goals of energy transition and sustainability in port infrastructure.

Financial Modelling System Using Deep Neural Networks (DNNs) for Financial Risk Assessments

ABSTRACTThe FOREX market assessment is a big challenge for investors and global risk managers. However, the present study uses daily multicurrency exchange rate returns data from 2007 to 2022 to estimate the learning returns performance of the proposed model to find a safe‐haven currency for optimal investment strategy. The categorical returns are classified into good returns (GRs), bad returns (BRs) and no returns (NRs). Therefore, the present study needs to use a one‐hot‐encoding function to convert a categorical dataset into a numeric format with TensorFlow. The present study proposes a deep neural network‐based multilayer perceptron (DNN‐based MLP) with a backpropagation algorithm to estimate the learning returns performance of the proposed model to find a safe‐haven currency for optimal investment strategy. The findings showed that currency exchange rate return 2 (CERR2) is relatively a safe‐haven currency than currency exchange rate return 1 (CERR1) and currency exchange rate return 3 (CERR3). Moreover, the findings also showed that the proposed model gives optimal learning return performance. This study may assist FOREX investors to modify their investment strategies under shed light of findings of the study. In addition, the findings of the present study may also support global risk managers to revisit their hedging strategies.

Deep learning for solving initial path optimization of mean-field systems with memory

We consider the problem of finding the optimal initial investment strategy for a system modelled by a linear McKean–Vlasov (mean-field) stochastic differential equation with delay, driven by Brownian motion and a pure jump Poisson random measure. The goal is to determine the optimal initial values for the system in the period [ − δ , 0 ] , where δ > 0 is a delay constant, before the system starts at t = 0. Due to the delay in the dynamics, the system will, after startup, be influenced by these initial investment values. It is known that linear stochastic delay differential equations are equivalent to stochastic Volterra integral equations. By utilizing this equivalence, we can find implicit expressions for the optimal investment. Moreover, we propose a deep neural network-based algorithm to solve the stochastic control problem with delay. Specifically, we employ a multi-layer feed-forward neural network for control modelling in the interval [ − δ , 0 ] , and use back-propagation to train the feed-forward neural network. The gradient of the loss function is computed using stochastic gradient descent (SGD) with respect to the weights of the network.

Dynamic spillover between green cryptocurrencies and stocks: A portfolio implication

Using the novel TVP-VAR connectedness approach, we investigate the spillovers of return and volatility as well as the portfolio diversifications between green cryptocurrencies and green stocks. The empirical findings demonstrate that there are considerable return and volatility spillovers across green cryptocurrencies and stocks. Stock indices such as Alternative Energy, Sustainable World Index, and Pollution Prevention act as net transmitters whereas Green Building stock and green cryptocurrencies act as net recipients of return and volatility spillovers. Sustainable World Index and Pollution Prevention stocks spread relatively stronger net spillovers to other green stocks and cryptocurrencies. The overall spillover effects and hedging costs become higher during the COVID-19 pandemic and the Russia-Ukraine war. Utilizing green cryptocurrencies like Cardano and Stellar Lumens as hedges for green stocks can provide superior risk reduction effectiveness. Our findings can offer practical implications for investors, portfolio managers, and regulators in developing their optimal investment and risk management strategies.

Optimal environmental investment strategies for enterprise green technology innovation: An empirical study based on multiple drive models

Enterprise green technology innovation (GTI) is vital for global sustainable development. However, the optimal strategies are needed to understand how environmental investments (EIs) impact enterprise GTI. This study adopts multiple drive models to explore the impact of EIs on the GTI of A-share listed enterprises in China from 2008 to 2022. Our results show that EIs significantly promote enterprise GTI, and these findings are robust. Heterogeneity analysis reveals that non-state-owned enterprises (non-SOEs) and enterprises in the eastern and western regions benefit more from EIs in promoting GTI. Labor-intensive combinations of EIs contribute to the growth of enterprise GTI quantity, while technology-intensive combinations of EIs are detrimental to the growth of enterprise GTI quality. Specifically, the intermediary conduction mechanism identifies that EIs substantially enhance enterprise GTI through financial constraints, research and development (R&D) investment, and environmental awareness. The threshold test mechanism demonstrates that EIs inhibit enterprise GTI when the price-to-book (P/B) ratio crosses a certain threshold; however, EIs promote enterprise GTI once the book-to-market (B/M) ratio crosses the threshold. Our findings can provide valuable references for governments and enterprises, helping to promote environmentally sustainable development and economic growth.

Optimal investment strategies and intergenerational risk sharing for target benefit pension plans under habit formation

This paper investigates a stochastic model of a continuous-time target benefit pension system with habit formation, where members' contributions are predetermined and pension payments depend on the financial condition of the system. Moreover, risk sharing among different generations is considered and we incorporate the habitual benefit payment process into the plan manager's objective. Concretely, the plan manager aims to minimize the deviation between actual payments and habitual payments, which can minimize the combined benefit-risk (i.e. deviation from the habitual target) and intergenerational transfers effectively. Furthermore, the pension fund is allowed to invest in a risk-free asset and a risky asset. By employing the martingale method, we derive the optimal investment strategy and the benefit adjustment strategy explicitly. Finally, numerical analysis is provided to illustrate the effects of model parameters on the optimal strategies.

DEFINING COMPONENTS OF THE METHODOLOGICAL PLATFORM FOR FORMING A BUSINESS PORTFOLIO OF A COMPANY IN THE UPDATED FORMAT OF MODERN DEVELOPMENT

The article is devoted to the analysis of the economic and operational imperatives of forming a business portfolio for a development company in the construction sector. A successful business portfolio management strategy requires the integration of financial, organizational, and technological aspects to ensure the sustainability and competitiveness of the business. In modern conditions, real estate development is one of the key factors that determines the dynamics of enterprise development, as it includes a comprehensive approach to asset management, from planning and financing to the construction and operation of objects. The theoretical and methodological foundations of the genesis of development at the current stage of the construction market's evolution have been analyzed.The methodological platform for forming a business portfolio should be based on the principles of rational resource management, risk analysis, and technological optimization. Changes in development activities require the active use of digital tools and a comprehensive approach to managing residential, commercial, and industrial properties, which allows for the maximization of profitability and minimization of risks.The article discusses the main stages of portfolio formation, such as strategic planning, selection of investment objects, and their integration into the overall structure of the enterprise. An economic and mathematical formalization of the process is also provided. For the successful operation of a development company, it is crucial to ensure coordinated work at all stages of the project — from planning and financing to construction and commissioning of the facilities.Particular attention is paid to the methods of economic and mathematical modelling (EMM) and quantitative risk analysis, which have become the basis for the development of the latest asset management strategies. The study analyses 35 different techniques. Each methodology offers unique tools for the effective management of development projects that allow forecasting financial flows, determining optimal investment strategies, and building the best plans for the development of a real estate portfolio. The specific methods used to value residential, commercial and industrial real estate are also discussed, taking into account their different levels of risk and return.It is important to note that the updated methodological platform is suitable for adaptation to the latest technologies and digital tools. This includes the introduction of a project management system, the use of artificial intelligence technologies to analyse large amounts of data, and the use of analytical tools to predict market trends. This approach helps to optimise asset management in a changing market environment. The analysis of the main components of the business portfolio formation platform also showed that important factors for the successful implementation of development projects are the speed of response to market changes, flexibility of management decisions, and the ability to minimise risks at all stages of the project.

Hydrogen production from non-potable water resources: A techno-economic investment and operation planning approach

The production of hydrogen through water electrolysis facilitates large-scale energy storage, provides ancillary services, and supports the decarbonization of industries with hard-to-reduce emissions. As renewable energy adoption expands, the demand for these applications is increasing. However, water electrolysis currently faces challenges in cost competitiveness compared to other hydrogen production methods. Additionally, its reliance on potable water sources places additional strain on freshwater reserves. This study addresses these issues by exploring the economically optimal investment and operational strategy for hydrogen production using non-potable water sources. The goal is to maximize net profit through mathematical optimization, utilizing three advanced electrolysis technologies: alkaline electrolysis, proton exchange membrane electrolysis, and solid oxide electrolysis. The study examines three non-potable water sources: seawater, urban wastewater effluent, and rainwater. The model takes into account electricity market values from day-ahead and balancing markets, as well as the market values for hydrogen, oxygen, freshwater, and mixed solid salt. Two scenarios are analysed, reflecting varying levels of uncertainty in electricity price forecasts. Each scenario includes nine case studies, representing various combinations of water sources and electrolysis technologies. The results indicate that alkaline electrolysis and proton exchange membrane electrolysis are financially viable technologies, with potential annual net profits of up to 6.4 and 6.2 million euros, respectively. In contrast, solid oxide electrolysis incurs a negative net profit across all scenarios and is not economically viable under the given conditions. The main revenue sources are hydrogen sales and combined up-balancing and down-balancing services in electricity markets. Participation in the balancing market constitutes a significant portion (35 to 61%) of the total revenue in all cases with positive net profits, making it critical for economic viability. Rainwater is identified as the most cost-effective water source for hydrogen production. However, the costs associated with water treatment and brine management are minimal, contributing only 0.7 to 3.7% to the total cost of hydrogen production. Thus, differences in net profit are primarily attributed to the type of electrolysis technology used.

The Application of Asset Pricing Models in the Capital Market

With the development of China's financial and capital markets, more and more investors will choose to use different asset pricing models to analyze the effectiveness of their investments. Under the background of efficient markets hypothesis (EMH), this paper will use Fama-French three-factor model, GARCH family model and Heston model to analyze the validity and feasibility of these three commonly used models in Chinese market. Through empirical analysis, descriptive statistics and other research methods, it is found that all three models are effective but have certain limitations. It is found that the Fama-French three-factor model is too dependent on the market. The establishment of the GRACH family model is too complicated due to too many influencing factors in the market; and the time lag of the Heston model. All three models require investors to include more model analysis to get the optimal investment strategy. Therefore, this paper draws the definition of behavioral finance at the end of the paper, according to which investors' decisions can be further analyzed.

Cybersecurity investments in supply chains with two-stage risk propagation

Cyber-attacks present a significant threat to supply chains as their nodes are directly or indirectly vulnerable to risk propagation at various stages. The risk level varies depending on the type of attack. A cybersecurity insurance offers a practical method to mitigate this risk, and it is crucial to determine optimal cybersecurity investments for all supply chain nodes. Previous studies have overlooked the joint impact of the attack type, two-stage risk propagation, and cybersecurity insurance in optimizing cybersecurity investments. This paper addresses this research gap by examining optimal investments under targeted and opportunistic attacks in a two-stage supply chain using game theory. The findings indicate that optimal investments differ based on the type of attack. For instance, retailers should invest more in cybersecurity under opportunistic attacks, while suppliers need to spend more under targeted attacks. Additionally, the results show that under opportunistic attacks, members should reduce their investments. Conversely, under targeted attacks, investments should initially increase and then stabilize. In the case of opportunistic attacks, suppliers and retailers should prioritize reconfiguring their systems over investing heavily in cybersecurity. The model presented in this paper demonstrates that not all cyber risks are worth defending against and that cybersecurity insurance for the entire supply chain can be more cost-effective than addressing cybersecurity risks individually. The paper also explores the impact of joint decisions on cybersecurity insurance when firms are unwilling to invest individually. The insights obtained enable supply chains to identify their optimal cybersecurity investment strategies effectively.

Life-cycle planning with CEV model and time-inconsistent preferences

In this paper, we investigate an optimization problem for a wage earner seeking to maximize expected utilities until retirement by choosing optimal consumption, investment, and life insurance purchase strategies. The constant elasticity of variance (CEV) model is adopted to describe the price process of the risky asset. Additionally, we assume that the wage earner has time-inconsistent preferences. This makes the wage earner discount her payoff by a non-constant discount rate. Applying the dynamic programming principle, we have derived the Hamilton-Jacobi-Bellman (HJB) equation corresponding to the optimization problem. Furthermore, we present semi-analytical expressions for optimal strategies and value functions in three cases: the benchmark model with time-consistent preferences, the naive and sophisticated wage earners with time-inconsistent preferences. Finally, illustrations of the optimal solutions and some economic insights are provided in the numerical examples.

Optimal investment and reinsurance strategies for an insurer with regime-switching

Optimal investment and reinsurance strategies for an insurer with regime-switching

Optimal consumption and investment in pooled annuity funds with and without fund managers

In this paper, we study two schemes of pooled annuity funds: pools with and without fund managers. In the pool without managers, there are no artificial rules or management cost and we introduce Nash equilibrium to depict the simultaneous non-cooperative game among participants. Given others' strategies, participants choose optimal consumption and investment strategies to maximize their own utility. In the pool with managers, the fund manager makes artificial rules for consumption and investment, ensuring cooperation among participants. The manager then determines optimal consumption withdrawal and investment strategies to maximize the total utility of all participants. By using variational methods and recursive algorithms, semi-analytical solutions in both pools are obtained. Due to prisoner's dilemma, larger pools without managers induce more intense competition in consumption and reduce utility. Thus, there exists an optimal pool size and only homogeneous participants form the pool. Meanwhile, larger pools with managers diversify investment and longevity risks more sufficiently and the subsidy effect among participants is mitigated. Therefore, the perfect pool with infinite participants is recommended as the optimal pool. Moreover, the preference between the two optimal pools depends on risk aversion degree, management cost and flexibility in selecting the strategies.

Robust optimal reinsurance and investment strategy for an insurer and a reinsurer with default risks and jumps

In this article, we analyze a robust optimal reinsurance and investment problem in a model with default risks and jumps for a general company which holds shares of an insurer and a reinsurer. The insurer’s surplus is characterized by a diffusion model and the insurer has the opportunity to buy proportional reinsurance from the reinsurer. Moreover, the insurer can invest in a risk-free asset (bank account), a risky asset (stock), and a defaultable bond. Meanwhile, the reinsurer can also invest in a risk-free asset and another risky asset. The price dynamics of the risky asset is assumed to follow a jump-diffusion model. What is more, the general company is concerned about the ambiguity and aims to find a robust optimal reinsurance and investment strategy. The objective of the general company is to maximize the minimal expected exponential utility of the weighted sums of the insurer’s and the reinsurer’s terminal wealth. Applying stochastic dynamic programming approach, we first establish the robust HJB (Hamilton-Jacobi-Bellman) equations for the post-default case and the pre-default case, respectively. Furthermore, we obtain the robust optimal strategy explicitly and present the corresponding verification theorem. Finally, we give some numerical examples to demonstrate the influences of model parameters on the robust optimal strategy.