Optimal Consumption Problem Research Articles

Robustness meets co-jumps: optimal consumption and portfolio choice with derivatives

In this paper, we study a robust, dynamic, continuous-time optimal consumption and portfolio allocation problem for investors with recursive preferences who have access to both stock and derivatives markets. We assume the stock price process follows a stochastic volatility model, with instantaneous precision as the unique state variable, allowing for discontinuities in all the dynamics. We obtain a closed-form approximate solution up to a system of ODEs to the optimization problem for a non-unitary value of the elasticity of intertemporal substitution of consumption, being able to derive an exact solution as a particular case. Our theoretical findings show that the optimal policies are remarkably affected by the ambiguity-aversion parameters to diffusive and jump risks. A detailed numerical analysis confirms the effectiveness of our theoretical results on real data. Finally, we prove that investors who do not believe in ambiguity may suffer considerable wealth losses.

The role of health in consumption and portfolio decision-making: Insights from state-dependent models

In this paper, we study an optimal consumption and asset allocation problem accounting for the fact that individuals’ utility differs across various health states. Our study is based on the assumption that an individual’s health status evolves through a semi-Markov process, where the transition probabilities are contingent on both the present state and the duration spent in that state. The optimal form of stock investment and of consumption is determined analytically. The optimal consumption level is significantly shaped by the integration of health-related factors and can be represented as the inverse of the marginal utility function with respect to time and state price density. Additionally, we introduce a Lagrangian multiplier that can be derived by solving a fixed point problem. While our optimal solutions are applicable to a wide range of utility functions, we provide numerical illustrations specifically using the power utility function in a model encompassing three distinct health states. Transition probabilities are estimated from real data collected by the China Insurance Regulatory Commission (CIRC), using a high-order polynomial Perks formula. We find that the investor’s consumption is higher when health is good, but lower when care is needed.

Investment–consumption optimization with transaction cost and learning about return predictability

In this paper, we investigate an investment–consumption optimization problem in continuous-time settings, where the expected rate of return from a risky asset is predictable with an observable factor and an unobservable factor. Based on observable information, a decision-maker learns about the unobservable factor while making investment–consumption decisions. Both factors are supposed to follow a mean-reverting process. Also, we relax the assumption for perfect liquidity of the risky asset through incorporating proportional transaction costs that are incurred in trading the risky asset. In such way, a form of friction posing liquidity risk to the investor is examined. Dynamic programming principle coupled with an Hamilton–Jacobi–Bellman (HJB) equation are adopted to discuss the problem. Applying an asymptotic method with small transaction costs being taken as a perturbation parameter, we determine the frictional value function by solving the first and second corrector equations. For the numerical implementation of the proposed approach, a Monte-Carlo-simulation-based approximation algorithm is adopted to solve the second corrector equation. Finally, numerical examples and their economic interpretations are discussed.

Q-learning based scheduling method for continuous pickling process of titanium strips

This article addresses the energy consumption optimization problems of the pickling process for titanium strip manufacturing. The hybrid flow shop scheduling schemes for the pickling process of titanium strips are designed, and a novel shop scheduling method based on reinforcement learning is proposed for the pickling process of titanium strips. In the scheduling scheme, the pickling chemical treatment process of titanium strips are described as an asymmetric hybrid flow shop scheduling problem (AHFSP), and a mathematical model containing a temperature structure is established with the optimization objectives of minimizing pickling time and energy consumption. Based on the proposed scheduling scheme, a novel shop scheduling method based on reinforcement learning for the titanium strip pickling process is proposed. First, a mixed integer linear programing model for the mixed flow shop scheduling problem is established. Second, the flow shop scheduling problem with sequential energy consumption decisions is approximated as an asymmetric traveling sales-man problem (ATSP). Finally, the ATSP is described as a Markov decision processes (MDP), and a Q-learning based scheduling method for titanium strip pickling shops is proposed. Finally, the effectiveness of the proposed method is verified by examples, and the scheduling scheme can reduce the energy consumption by 16.61% on average while maintaining the schedule, which improves the productivity and economic efficiency.

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].

A dynamic game approach for optimal consumption, investment and life insurance problem

AbstractIn this paper, we consider a multi-agent portfolio optimization model with life insurance for two players with random lifetime under a dynamic game approach. Each player is a price-taker and invests in the market to maximize her own utility for consumption and bequest. The market is complete and consists of n different assets, of which $$n-1$$ n - 1 are risky with prices driven by Geometric Brownian motion, while one is risk-free. We analyze both the non-cooperative and cooperative scenarios, and by considering the family of CRRA utility functions, we determine the closed-form expressions of the optimal consumption, investment, and life insurance for both players. A sensitivity analysis is provided both to illustrate the impact of the biometric and risk aversion parameters on the optimal controls and to compare the non-cooperative strategies with the cooperative ones. As a result, we suggest that cooperation favors the consumption optimality, while non-cooperation promotes the coverage of the risk of death.

Optimal payout strategies when Bruno de Finetti meets model uncertainty

Model uncertainty is ubiquitous and plays an important role in insurance and financial modeling. While a substantial effort has been given to studying optimal consumption, portfolio selection and investment problems in the presence of model uncertainty, relatively little attention is given to investigating optimal payout policies taking account of the impacts of model uncertainty. As one of the early attempts, this paper studies the optimal payout control problem under the classical risk model taking into account of model uncertainty about the claims arrival intensity. We aim to provide insights into understanding optimal decisions incorporating model uncertainty and to examine key impact of model uncertainty. We find that the optimal strategy robust to model uncertainty is of a band type. However, the presence of the model uncertainty alters the qualitative behavior of the optimal strategy in the sense that the optimal robust policy is no longer a barrier strategy for some particular cases. We provide numerical examples to illustrate the theoretical results and examine the impact of model uncertainty on optimal payout policies. We also provide examples that use real insurance data for calibration. We discover that the decision maker takes more conservative strategies under model uncertainty, which is consistent with the findings in the economic field and has not been addressed in the existing optimal payout problems without model uncertainty.

A long-term optimal consumption and investment problem with partial information

A long-term optimal consumption and investment problem with partial information

CSAT‐FRMET: An energy‐efficient hybrid FiWi network‐based 5G model

AbstractHybrid fiber wireless (FiWi) access networks seek to combine the vast amount of bandwidth that is available for optical networks and wireless network mobility; hence, it favors larger bandwidth request but cause the highly nonlinear lagrangian dual problem that decrease energy‐efficient network resilience. Hence, a novel Ceplato‐SAT3 model has been proposed in which the SAT3 algorithm locates the optical network unit (ONU) in an optimal position with high‐speed cost‐efficient placement and weight factor introduced into the position update to improve the exploitation and exploration capability of the algorithm. To prioritize the large bandwidth request during resource allocation, gradient priority justifier requests (GPJR) has been utilized and a novel messaging technique termed flow‐random‐message‐exchanger‐topology (FRMET) provides the index for these prioritized requests depending on QoS parameters such as notification control, reflective QoS attribute (RQA), flow bit rates and maximum packet loss rate thereby decreasing the overhead and eliminate nonlinear langrage dualand perform O2U scheduling to reduce network resilience however synchronization between different ONU clocks may cause upstream data fatal crash at the optical line terminal (OLT). Hence, curl‐trio‐opt control mechanism has been proposed in which the minimization problem is transformed into a joint optimization problem of energy consumption, traffic demand, network requests, and service flow requests by the Lyapunov technique thereby minimizing the upstream data fatal lash. The proposed model has been implemented in Python and the output obtained showed better performance in terms of ONU arrangement, throughput, energy consumption, computation, latency, and error.

Equilibrium multi-agent model with heterogeneous views on fundamental risks

This paper investigates an equilibrium-based multi-agent optimal consumption and portfolio problem incorporating uncertainties on fundamental risks, where multiple agents have heterogeneous (conservative, neutral, aggressive) views on the risks represented by Brownian motions. Each agent maximizes its expected utility on consumption under its subjective probability measure. Specifically, we formulate the individual optimization problem as a sup–sup–inf problem, which is an optimal consumption and portfolio problem with a choice of a probability measure. Moreover, we provide an expression of the state-price density process in a market equilibrium, which derives the representations of the interest rate and the market price of risk. To the best of our knowledge, this is the first attempt to investigate the multi-agent model with heterogeneous views on the risks by considering a market equilibrium and solving sup–sup–inf problems on the choice of a probability measure. We emphasize that the setting, where each agent has heterogeneous views on different risks, incorporates a special case where each agent has only conservative or neutral views on risks with different degrees of conservativeness. Also, the setting includes the case where the agents have aggressive views on risks, commonly observed as bullish sentiments in the financial markets in the monetary easing after the global financial crisis and particularly in the COVID-19 pandemic. Finally, we present numerical examples of the interest rate model, which show how heterogeneous views of the multiple agents on the risks affect the shape of the yield curve.

Multi-Objective Optimization with PCM integration and delayed cooling strategy for high-rate discharge applications

The thermal safety of lithium-ion batteries has been a significant concern in the industry, prompting a pressing need for research to ensure efficient and energy-saving operation of energy storage battery's thermal management system. This study focuses on addressing the multi-objective optimization problem of heat dissipation coupling energy consumption in battery packs under high discharge rate with a maximum temperature (Tmax), a maximum temperature difference (ΔT) and the pump energy consumption (P) as objectives. The Kriging interpolation and CRITIC weighting method are used for multi-objective optimization to determine the optimum solution objectively. The results indicate that increasing the diameter of the liquid cooling pipe (X) and the coolant inlet velocity (vin) both contribute to reducing the maximum temperature of system. However, these changes have negative impacts on temperature uniformity within the battery pack and the energy consumption of the water pump. The above rule is reversed when considering the impact of initiation time of coolant flow (T), which in addition can lead to exhaustion of latent heat of CPCM and insufficient cooling capacity and thus potential overheating of the battery pack. According to the CRITIC weighting method analysis, the index weights of Tmax, ΔT and P are 40.21%, 32.01% and 27.79%, respectively. Further analysis reveals that the optimal comprehensive performance of the battery pack thermal management system is achieved when X = 3.875 mm, vin = 0.4 m/s, and T = 537.5 s, corresponding the P of 2.53 J, Tmax of 309.32 K and ΔT of 2.41 K, both falling within the specified technical requirements at a discharge of 4 C . The latent heat of the phase change material in the battery pack has been recovered at this stage, providing sufficient cooling capacity for the next cycle of charging and discharging.

Controller Design for Optimizing Fuel Consumption of Truck Platoon on Hilly Roads

Platoons consisting of automated and connected vehicles show great potential in reducing fuel or energy consumption. However, the fuel consumption optimization problem for truck platoons traveling on hilly roads has not been investigated thoroughly. To address that problem, a hierarchical control framework is proposed in this paper as follows: (1) The supervising layer is responsible for generating the fuel-oriented optimal speed profile based on the terrain information; (2) The distributed layer consists of an LQR feedback controller, a DMPC feedforward controller and a tube integration method to integrate the two controllers; it receives the optimal speed profile from the supervising layer and yields the control input to the individual vehicle. In this paper, a novel optimal speed profile generation method is proposed, a novel integration of tube method is applied, and the stability performance is analyzed rigorously. Simulations based on a real hilly road are conducted, and the performance of the proposed controller is evaluated regarding the platoon stability, fuel consumption and computation efficiency. The results of the simulation show that the controller is capable of maintaining the string stability of the truck platoon and reducing fuel consumed on hilly roads while improving computation efficiency.

Optimal Consumption and Investment Problem under 4/2-CIR Stochastic Hybrid Model

In this paper, we investigate the optimal consumption and investment problem under the expected utility maximization criterion. It is supposed that the financial market consists of a risky asset and a risk-free asset, and the risky asset prices follow the 4/2 Cox–Ingersoll–Ross (CIR) stochastic hybrid model. The investment objective is to obtain an optimal consumption–investment strategy by maximizing the objective function. The closed-form expression of the optimal consumption–investment strategy is obtained by using optimal control theory and the corresponding Hamilton–Jacobi–Bellman (HJB) equation under the power utility function. In addition, we present a numerical example to illustrate the influence of model parameters on the optimal consumption–investment strategy.

Optimal investment, consumption and life insurance purchase with learning about return predictability

This paper studies the optimal investment, consumption and life insurance purchase problem for a wage earner under the condition that the return on the risky asset is predictable. We assume that the market price of risk is an affine function consisting of an observable and an unobservable factor that follow the O-U processes, while the evolution of the interest rate is described by the Vasicek model. The optimal investment, consumption and life insurance strategies and the corresponding value function are derived by adopting the filtering technique and the dynamical programming principle approach. In addition, for comparative analysis, the suboptimal strategies and the utility losses are presented when the wage earner ignores learning or the randomness of the interest rate. Finally, some numerical examples are presented to illustrate the results.

Optimal Consumption Under a Habit-Formation Constraint: The Deterministic Case

We formulate and solve a deterministic optimal consumption problem to maximize the discounted constant relative risk aversion utility of an individual’s consumption-to-habit process assuming they only invest in a riskless market and that they are unwilling to consume at a rate below a certain proportion of their consumption habit. Increasing increases the degree of addictiveness of habit formation, with (respectively, ) corresponding to nonaddictive (respectively, completely addictive) model. We derive the optimal consumption policies explicitly in terms of the solution of a nonlinear free-boundary problem, which we analyze in detail. Impatient individuals (or, equivalently, those with more addictive habits) always consume above the minimum rate; thus, they eventually attain the minimum wealth-to-habit ratio. Patient individuals (or, equivalently, those with less addictive habits) consume at the minimum rate if their wealth-to-habit ratio is below a threshold and above it otherwise. By consuming patiently, these individuals maintain a wealth-to-habit ratio that is greater than the minimum acceptable level. Additionally, we prove that the optimal consumption path is hump-shaped if the initial wealth-to-habit ratio is either (1) larger than a high threshold or (2) below a low threshold and the agent is more risk seeking (that is, less risk averse). Thus, we provide a simple explanation for the consumption hump observed by various empirical studies.

Reinforcement Learning for Model Problems of Optimal Control

The functionals of dynamic systems of various types are optimized using modern methods of reinforcement learning. The linear resource allocation problem, as well as the optimal consumption problem and its stochastic modifications are considered. In the reinforcement learning strategy gradient methods are used.

Film dance creation practice supported by Cyber Physical System.

The traditional eight arts include film and dance. Dance is often included in the creation of films. With the progress of the times, dance has shown unprecedented vitality in film. This also puts forward higher requirements for shooting technology in film creation. To solve the contradiction between high performance of equipment and energy sensing, a new energy aware scheduling framework is proposed based on Cyber Physical System, which utilizes the balance between performance and energy consumption optimization, and uses allocation technology and list scheduling to ensure energy constraints. Besides, a highly energy-efficient and stable scheduling algorithm for film creation is constructed. The algorithm problems are mainly divided into functional safety requirements, verification problems, and energy consumption optimization problems under functional safety. The experimental results show that the system can obtain better schedulability at a lower time complexity and reasonably reflect the dynamic and static energy constraints ratio. The basic framework system based on dynamic step size also achieves better time performance than other step sizes. According to the experiment's findings, the energy consumption of all scheduling components is relatively low and can be maintained within a specific range. The research and analysis of this study can provide a theoretical reference for the equipment algorithm of film dance creation practice, promote interaction with technical practice, and assist in promoting the development process of film dance creation.

Maximum Principle for Stochastic Control of SDEs with Measurable Drifts

In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation process (in the Sobolev sense) of the controlled diffusion. Since the drift coefficient is not smooth, the representation is given in terms of the local time of the state process. Then we construct a sequence of optimal control problems with smooth coefficients by an approximation argument. Finally, we use Ekeland’s variational principle to obtain an approximating adjoint process from which we derive the maximum principle by passing to the limit. The work is notably motivated by the optimal consumption problem of investors paying wealth tax.

Robust consumption for individuals with pessimistic survival beliefs

As some literature reveal, young people generally keeps pessimistic survival beliefs, and individuals usually make decisions based on their expectations instead of the experience data. Motivated by this idea, we study the optimal consumption problem for individuals with ambiguity aversion about their mortality. Closed-form robust consumption policy before retirement is obtained by solving the HJB equation by employing the dynamic programming principle. The result tells us that pessimistic survival beliefs, together with interest rate, risk attitude, and expectations for the retirement, play an important role on the consumption and saving decision-making. Reducing interest rates can promote consumption, but the impact is not significant. Both mortality and risk aversion level have significant impacts on the consumption. Too much pessimistic survival beliefs or too much low risk aversion level would lead to overconsumption.

Energy Management Strategies for Hybrid Loaders: Classification, Comparison and Prospect

As one of the effective and crucial ways to achieve the energy saving and emission reduction of loaders, hybrid technology has attracted the attention of many scholars and manufacturers. Selecting an appropriate energy management strategy (EMS) is essential to reduce fuel consumption and emissions for hybrid loaders (HLs). In this paper, firstly, the application status of drivetrain configuration of HLs is presented. Then, the working condition characteristics of loaders are analyzed. On the basis of this, the configurations of HLs are classified, and the features and research status of each configuration are described. Next, taking the energy consumption optimization of HLs as the object, the implementation principle and research progress of the proposed rule strategy and optimization strategy are compared and analyzed, and the differences of existing EMSs and future development challenges are summarized. Finally, combining the advantages of intelligent control and optimal control, the future prospective development direction of EMSs for HLs is considered. The conclusions of the paper can be identified in two points: firstly, although the existing EMSs can effectively optimize the energy consumption of HLs, the dependence of the strategy on the mechanism model and the vehicle parameters can reduce the applicability of the strategy to heterogeneous HLs and the robustness to a complex working condition. Secondly, combining the advantages of intelligent control and optimal control, designing an intelligent EMS not depending on the vehicle analytical model will provide a new method for solving the energy consumption optimization problem of HL.