Optimal Investment Model Research Articles

Optimal Consumption and Investment with Independent Stochastic Labor Income

We develop a new dynamic continuous-time model of optimal consumption and investment to include independent stochastic labor income. We reduce the problem of solving the Bellman equation to a problem of solving an integral equation. We then explicitly characterize the optimal consumption and investment strategy as a function of income-to-wealth ratio. We provide some analytical comparative statics associated with the value function and optimal strategies. We also develop a quite general numerical algorithm for control iteration and solve the Bellman equation as a sequence of solutions to ordinary differential equations. This numerical algorithm can be readily applied to many other optimal consumption and investment problems especially with extra nondiversifiable Brownian risks, resulting in nonlinear Bellman equations. Finally, our numerical analysis illustrates how the presence of stochastic labor income affects the optimal consumption and investment strategy. Funding: A. Bensoussan was supported by the National Science Foundation under grant [DMS-2204795]. S. Park was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea, South Korea [NRF-2022S1A3A2A02089950].

Explicit Solution of the Mean-variance Optimal Investment Model for Defined-contribution Pension under Non-extensive Statistical Mechanics

Explicit Solution of the Mean-variance Optimal Investment Model for Defined-contribution Pension under Non-extensive Statistical Mechanics

A Novel Hybrid Power-Grid Investment Optimization Model with Collaborative Consideration of Risk and Benefit

Power-grid investment (PGI) optimization is crucial for boosting investment performance, lowering investment risks, and assuring the sustainable development of power-grid businesses. However, existing studies, which primarily concentrate on financial aspects, have not adequately considered the risk and benefit factors in the process of PGI. In this context, this research suggests a novel hybrid PGI optimization model that collaboratively accounts for the risks and benefits. In the first step, risk and benefit indicator systems for PGI are built, and a comprehensive evaluation model based on the Bayesian best–worst method and TOPSIS is suggested. In the second stage, a PGI optimization model considering the investment amount, power demand, and low-carbon restrictions is further developed based on the evaluation results. Furthermore, the incomprehensible but intelligible-in-time logic algorithm is adopted to solve the problem. By conducting an empirical analysis of ten projects within a power-grid company, the optimal investment plan and a differentiated investment portfolio strategy are obtained by adjusting the key elements.

Mean-Variance Investment Without Risk-Free Assets in PT Company Shares PT Ace Hardware (Aces.Jk), PT Mayora Indah (Myor.Jk), PT Bri (Bbri.Jk), PT Siloam Hospital (Silo.Jk), PT Eterindo Wahanatama (Etwa.Jk)

Portfolio is a form of strategy that investors often apply in risky investment conditions. The essence of portfolio construction is to allocate funds to various investment options to minimize investment risk. Therefore, the aim of this discussion is to construct an investment portfolio of several shares using an average variable portfolio optimization model without risk-free assets. To obtain an optimal portfolio, a mean-variance investment optimization model without risk-free assets or what is called the Basic Markowitz model is used. This involves investors measuring the risk of an asset using its “variance” and then comparing it to the asset's average. It is hoped that this discussion can help investors to obtain an optimal portfolio, especially from the five selected shares.

Theoretical and practical research on mathematical modeling of economy and finance based on artificial intelligence

Abstract In the context of the rapid development of big data technology, developing an artificial intelligence economy is beneficial to China’s economic transformation, industrial upgrading, and enhancing international competitiveness. This paper first constructs a financial mathematical model of the AI economy based on the theoretical foundation of financial mathematics. The structure of the financial mathematical model mainly consists of three parts: portfolio model, capital asset pricing model, and financial derivatives pricing model. To address the problem of the unstable development of China’s AI economy, the theoretical framework of investment risk management is constructed, which can help investors intelligently implement investment risk management plans and implement investment risk management countermeasures and measures. Finally, to verify the performance of the risk investment optimization model and intelligent algorithm proposed in this chapter, three investment scales will verify the investment risk management capability based on the portfolio model. The results show that the convergence performance of the portfolio model is 0.2025, 0.4021, and 0.4391 for three investment sizes of 2, 4, and 9, and the penalty coefficients are 1.5, 28, and 0.2, respectively. At the beginning of the iteration, the investment risk is high, and the convergence speed of the portfolio model is higher than the capital asset pricing model and the financial derivatives pricing model. This study applies it to solve financial optimization problems, including portfolio, stock forecasting, risk management, and many other fields, and provides a better solution to the optimization decision problem of the portfolio.

Renewable energy communities optimal design supported by an optimization model for investment in PV/wind capacity and renewable electricity sharing

The EU Renewable Energy Directive 2018/2001 (RED II) has unlocked the participation of local citizens and authorities in collective renewable energy projects through the concept of Renewable Energy Communities (REC). In this context, the present study proposes an optimization model to support REC's investment decisions on the renewable generation portfolio and operational electricity sharing management.The model presented follows an annualized investment optimization approach considering that one REC member can invest in additional renewable generation. A case study of a REC with three members is presented in a framework of four scenarios and results are discussed using the levelized cost of electricity (LCOE) and the marginal realized price concepts. A sensitivity analysis is also performed to address the interannual variability of the solar and wind resources.In the base case scenario, which corresponds to the site-specific conditions of the investing REC member, an overall net revenue of 87 k€/year was computed. The sensitivity analysis for this scenario showed that the investment is more sensitive to the solar resource, with revenues changing between −3.3% and 0.1% in comparison with the average resource availability.This paper contributes to the existing literature by identifying the main drivers behind the optimal investment decision of a REC, which result from the relationship between the marginal realized price and the levelized cost of the electricity generated by each renewable technology. The results supported by the present model reinforce the benefits of RECs as enablers for the deployment of renewable generation, thus contributing to the decarbonization of the energy systems.

A Generalized Finite Difference Method for Solving Hamilton–Jacobi–Bellman Equations in Optimal Investment

This paper studies the numerical algorithm of stochastic control problems in investment optimization. Investors choose the optimal investment to maximize the expected return under uncertainty. The optimality condition, the Hamilton–Jacobi–Bellman (HJB) equation, satisfied by the value function and obtained by the dynamic programming method, is a partial differential equation coupled with optimization. One of the major computational difficulties is the irregular boundary conditions presented in the HJB equation. In this paper, two mesh-free algorithms are proposed to solve two different cases of HJB equations with regular and irregular boundary conditions. The model of optimal investment under uncertainty developed by Abel is used to study the efficacy of the proposed algorithms. Extensive numerical studies are conducted to test the impact of the key parameters on the numerical efficacy. By comparing the numerical solution with the exact solution, the proposed numerical algorithms are validated.

Contagion risks and security investment in directed networks.

We develop a model for contagion risks and optimal security investment in a directed network of interconnected agents with heterogeneous degrees, loss functions, and security profiles. Our model generalizes several contagion models in the literature, particularly the independent cascade model and the linear threshold model. We state various limit theorems on the final size of infected agents in the case of random networks with given vertex degrees for finite and infinite-variance degree distributions. The results allow us to derive a resilience condition for the network in response to the infection of a large group of agents and quantify how contagion amplifies small shocks to the network. We show that when the degree distribution has infinite variance and highly correlated in- and out-degrees, even when agents have high thresholds, a sub-linear fraction of initially infected agents is enough to trigger the infection of a positive fraction of nodes. We also demonstrate how these results are sensitive to vertex and edge percolation (intervention). We then study the asymptotic Nash equilibrium and socially optimal security investment. In the asymptotic limit, agents' risk depends on all other agents' investments through an aggregate quantity that we call network vulnerability. The limit theorems enable us to capture the impact of one class of agents' decisions on the overall network vulnerability. Based on our results, the vulnerability is semi-analytic, allowing for a tractable Nash equilibrium. We provide sufficient conditions for investment in equilibrium to be monotone in network vulnerability. When investment is monotone, we demonstrate that the (asymptotic) Nash equilibrium is unique. In the specific example of two types of core-periphery agents, we illustrate the strong effect of cost heterogeneity on network vulnerability and the non-monotonous investment as a function of costs.

A Heston local-stochastic volatility model for optimal investment–reinsurance strategy with a defaultable bond in an ambiguous environment

A Heston local-stochastic volatility model for optimal investment–reinsurance strategy with a defaultable bond in an ambiguous environment

Research on investment planning of power-hydrogen system considering the multi-stakeholder benefit

As the penetration of renewable energy sources continues to increase, the stability of the grid is being challenged. Solutions are needed to curb fluctuations in renewable energy generation and ensure a stable electricity supply. As a clean and efficient secondary energy source, hydrogen energy plays an important role in the power system. However, the development of hydrogen energy storage systems is currently limited by technology and costs, making it difficult to scale up. How to invest to make hydrogen storage economical is worth studying. This paper constructs a regional microgrid system, considering the economics of investment by renewable energy generators (REGs) and integrated energy operators (IEOs), and the sensitivity of the payback period under conditions of market adjustment and technological progress. A combination of the Gurobi and Particle Swarm Optimization (PSO) algorithm is used to solve the investment optimization model, and Shapley is used to allocate multi-intelligence benefits. The results show that: (1) the investment returns and payback periods of REG are within a reasonable range; (2) IEO is hardly economical in the presence of market price changes and technological advances. On this basis, this paper constructs a win-win investment model for REG and IEO and explores the distribution of benefits under their cooperation model. The results show an increase in return on investment of 0.34% for REG and 1% for IEO following investments by REG in partnership with IEO.

RETRACTED: Green investment mechanism considering supply chain risk aversion and negotiating power

• Offer to implement optimal decision in relation to green investment. • Two types of cost-sharing contract is considered. • Supply chain risk aversion is negatively related to green investment. In this paper, we study the green investment decision question in a rice supply chain composed of supply chain risk aversion (SCRA) planting firms and supply chain risk-neutral (SCRN) sellers. Under centralized and decentralized decision-making, we consider the two types of cost-sharing contract (CSC) namely the general (CSC) and the CSC considering the bargaining power. We study the influence of SCRA and construct the green investment optimization model for the rice supply chain. Our study shows that the green investment level in the decentralized rice supply chain is negatively correlated with the SCRA, while the SCRA is positively correlated with the green investment level regardless of the type of CSC. By comparing the two CSCs, we find that both contracts not only improve the expected utility of the rice supply chain but also enhance the green investment level of the rice supply chain. Under the bargaining game, the SCRA is positively correlated with the green investment level and cost-sharing ratio. On the other hand, the bargaining power is also positively correlated with the green investment level and cost-sharing ratio. Under certain conditions, the green investment level of the rice supply chain can be lower than that of the decentralized supply chain. Considering rice planting firms' SCRA and negotiation power, the bargaining CSC is the best under certain conditions.

Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations

Abstract This paper proposes a financial risk monitoring system based on partial differential equations. In this paper, a functional expression of risk measurement is proposed for the uncertainty of financial assets risk of financial institutions. In this paper, a partial differential equation model of asset price based on non-extensive statistical theory is established. At the same time, this paper establishes the optimal portfolio investment model with the restriction of risk measure under partial differential equation. The experimental study shows that the financial risk measurement method under the partial differential equation proposed in this paper fully considers the financial risk uncertainty of financial assets. It satisfies the axiomatic system of consistent risk measures.

Investment planning for earthquake-resilient electric power systems considering cascading outages

Earthquakes cause outages of power transmission system components due to direct physical damage and also through the initiation of cascading processes. This article explores what are the optimal capacity investments to increase the resilience of electric power transmission systems to earthquakes and how those investments change with respect to two issues: (1) the impact of including cascades in the investment optimization model and (2) the impact of focusing more heavily on the early stages of the outages after the earthquake in contrast to more evenly focusing on outages across the entire restoration process. A cascading outage model driven by the statistics of sample utility data is developed and used to locate the cascading lines. We compare the investment plans with and without the modeling of the cascades and with different levels of importance attached to outages that occur during different periods of the restoration process. Using a case study of the Eastern Interconnect transmission grid, where the seismic hazard stems mostly from the New Madrid Seismic Zone, we find that the cascades have little effect on the optimal set of capacity enhancement investments. However, the cascades do have a significant impact on the early stages of the restoration process. Also, the cascading lines can be far away from the initial physically damaged lines. More broadly, the early stages of the earthquake restoration process is affected by the extent of the cascading outages and is critical for search and rescue as well as restoring vital services. Also, we show that an investment plan focusing more heavily on outages in the first 3 days after the earthquake yields fewer outages in the first month, but more outages later in comparison with an investment plan focusing uniformly on outages over an entire 6-month restoration process.

A safety investment optimization model for power grid enterprises based on System Dynamics and Bayesian network theory

In recent years, frequent large-scale power grid accidents have caused serious economic losses and bad social impact, which has drawn great attention from power grid enterprises. As one of the key elements of production, safety investment plays an important role in improving the safety level and reducing accident loss. In this paper, System dynamics (SD) and Bayesian network (BN) are integrated to develop a novel safety investment optimization model for power grid enterprises, which takes into account the impact of safety investment factors on accidents and the interactions between them. Based on sensitivity analysis, critical safety investment factors are determined to form the subsystem of the SD model. Subsequently, the optimal safety investment strategy is determined by a three-step simulation. The simulation results show that there are barrel effects and a diminishing marginal utility in safety investment. The proposed safety investment optimization model is practical to provide technical supports and guidance for determining an effective safety investment strategy in power grid enterprises.

Lifetime consumption and investment with housing, deferred annuities and home equity release

We develop a life-cycle optimal investment and consumption model with deferred annuities, housing, mortgages and home equity release. The investor can hold cash, bonds, stocks, annuities and can invest in housing, through renting, purchasing, or a mix of both, with access to variable-rate mortgages. In retirement, the investor can access his housing equity through a form of home equity release called a home reversion contract. Transaction costs, taxes and management fees are explicitly included. The investor's risk preferences are represented by standard power utility derived from housing and non-housing consumption, both before and after retirement, and from bequest. We use multi-stage stochastic programming to solve the optimization problem numerically. Our results show that both non-housing and housing consumption may be higher in retirement when deferred annuities and home reversion are available than when they are absent. The bequest motive has little effect on home reversion and results in a small reduction in overall annuitization.

Optimal investment and reinsurance of insurers with lognormal stochastic factor model

<p style='text-indent:20px;'>We propose the stochastic factor model of optimal investment and reinsurance of insurers where the wealth processes are described by a bank account and a risk asset for investment and a Cramér-Lundberg process for reinsurance. The optimization is obtained through maximizing the exponential utility. Owing to the claims driven by a Poisson process, the proposed optimization problem is naturally treated as a jump-diffusion control problem. Applying the dynamic programming, we have the Hamilton-Jacobi-Bellman (HJB) equations and the corresponding explicit solution for the corresponding HJB. Hence, the optimal values and optimal strategies can be obtained. Finally, in numerical analysis, we illustrate the performance of the proposed optimization according to the results of the corresponding value function. In addition, compared to the wealth process without investment, the efficiency of the proposed optimization is discussed in terms of ruin probabilities.</p>

Transmission Grid Resiliency Investment Optimization Model With SOCP Recovery Planning

In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model.

Sensitivity and Joint Investment Analyses of a Multi-objective Investment Optimization Model of two Businesses in Ghana

This paper is a further development of an earlier work reported in the literature by the authors. In that work, the investment problems of two businesses in Ghana were formulated as biobjective optimization models in which their expected returns and risks were optimized simultaneously using real data from the two. The current work investigates the two models under a sensitivity analysis and about the potential benefits that a joint investment could hold for the two businesses. The rates of return parameters were identified as the most likely to vary over the period of the investments. Therefore, they were varied up and down by 5% and up and down by 10%, considered as reasonable levels of variation. A random selection procedure was employed to obtain two random sets of rates of return parameter values for the two businesses, from which expected return and risk values were obtained for each of the models. The results of running the models (in MATLAB) showed that the impact of parameter variations was not significant, as far as the Pareto optimal solutions which are the amounts to invest, were concerned; the objective function values of returns and variances varied however, since their coefficient values varied with the values of the parameters varied. The formulated joint model produced results that showed that a joint investment could be more profitable than separate investments, even though that had a much higher risk.

Flexibility from Combined Heat and Power: A Techno-Economic Study for Fully Renewable Åland Islands

As energy systems globally are transitioning into renewable energy, simultaneous targets of high self-sufficiency have led to complex system design proposals. While conventional technology solutions would reduce the complexity in theory, limitations in the potential outcome may exist. To address this dilemma, the work quantified the systemic value provided by a conventional solution; biomass combined heat and power (CHP) production, in terms of economic feasibility, provided flexibility and energy self-sufficiency. The analysis focused on the renewable energy integration of the Åland Islands, where the synergetic island energy system is heavily increasing the wind power capacity. While considering local fuel resource availability, multiple alternative energy system scenarios were constructed. To evaluate the scenarios, the work developed and validated a combined dispatch and investment optimization model. The results showed that the studied conventional approaches limited the achievable self-sufficiency in the power sector (80.6%), however, considerably increasing the value from the present state (18.5%). Second, compared to previous studies, the results indicated a low value from biomass CHP in the wind-based energy system. Instead, the combination of high wind capacity and power-to-heat enabled the best economic feasibility and high self-sufficiency, which could be further improved by lower electricity taxation.

Optimal investment in human capital under migration uncertainty

AbstractThis paper develops a model of optimal education investment under uncertainty for an agent with an emigration option. We distinguish between local (country‐specific) and global human capital and analyze the role of migration opportunities in human capital accumulation of different types. The analysis shows that human capital accumulation depends on the level of uncertainty and the transferability of human capital across countries. Allowing for human capital investment in the destination country and easier transferability of both local and global human capital exacerbate brain drain.