International portfolio choice under multi-factor stochastic volatility

Retirees meet a number of problems as they are growing older which needs persistent attention. Hence, without a doubt, the outcomes of the financial markets influence the choices that people make when nearing retirement. In our model, the stock price dynamics follow Geometric Brownian motion (GBM) and our goal was to optimize the expected discounted utility of consumption and terminal wealth whilst considering health expenses. The investment return process comprises risk free asset and risky assets, and the health expenses. We choose power utility functions where comprehensive solutions for Hyperbolic Absolute Risk Aversion (HARA) utility functions are obtained and optimal investment, consumption and health expenditure strategies are derived by applying dynamic programming and variable change technique on the Hamilton-Jacobi-Bellman (HJB) equations. In our numerical results it showed various effects of some economic and market parameters on the optimal investment, consumption and health expense strategies. The inflation price market risk governs the amount invested in stock, bond and also how much to be put in health to sustain a given period of the retiree's lifetime. As the health welfare rate R increases, the proportion of wealth invested in the stock increases. We also investigated the effects of the high correlation coefficients and low correlation coefficients on consumption and income rate respectively. As the constant variance discounting coefficient increases, seasoned enterprise annuity retirees decrease their allocation to the risky assets. Finally, a numerical example is presented to depict the effects of financial parameters on the optimal investment strategy with health expenditure.

sumption in period j, such that either the risk aversion index -u(x)/u'(x), or the risk aversion index -xu'(x)/u'(x), is a positive constant for all x > 0. In a second paper [6], it was further shown that this model, developed with the individual in mind, also gives rise to an induced theory of the firm under risk for the same class of utility functions. In the foregoing model, it was assumed that the individual's horizon was infinite (or known with certainty). In this paper, we consider the same basic model with three modifications. First, we postulate that the individual's, lifetime is a random variable with a known probability distribution. Second, we introduce a utility function intended to represent the individual's bequest motive. Third, we offer the individual the opportunity to purchase insurance on his life. It is found that when some or all of these modifications are made, all of the more important properties possessed by the optimal consumption and investment strategies under a certain horizon are preserved, albeit only under special conditions. In Section 2, the various components of the decision process are constructed. In the earlier model, the individual's objective was assumed to be the maximization of expected utility from consumption over time. Here, we postulate, more generally, that his objective is to maximize expected utility from consumption as long as he lives and from the bequest left upon his death. As before, the individual's resources are assumed to consist of an initial capital position (which may be negative) and a non-capital income stream. The latter, which may possess any time-shape, is assumed to be known with certainty and to terminate upon his death. In addition to insurance available at a fair' rate, the individual faces both financial opportunities (borrowing and lending) and an arbitrary number of productive investment opportunities. The interest rate is presumed to be known but may have any time-shape. The returns from the productive opportunities are assumed to be random variables, whose probability distributions may differ from period to period but are assumed to satisfy the no-easy-money condition. While no limit is placed on borrowing, the individual is required to be solvent at the time of his death with

Robust optimal reinsurance and investment strategies for an AAI with multiple risks

We investigate the optimal investment strategies of DC pension under stochastic volatility model using combined Heston-Hull-White (HHW) model with a constant income drawdown. The pension fund manager (PFM) aims to maximize the expected terminal utility of wealth in a complete market setting under constant relative risk aversion (CRRA). The goal of the PFM is to maintain the standard of living of the participants after retirement. We derive the HJB equation associated with the control problem and finally established the close form solution using stochastic dynamic programming principle (SDPP). The results show that the optimal investment and benefit payment strategies converge uniquely with time.

On optimal investment strategies for energy conservation

In this paper, a novel framework for the estimation of optimal investment strategies for combined wind-thermal companies is proposed. The medium-term restructured power market was simulated by considering the stochastic and rational uncertainties, the wind uncertainty was evaluated based on a data mining technique, and the electricity demand and fuel price were simulated using the Monte Carlo method. The Cournot game concept was used to determine the Nash equilibrium for each state and stage of the stochastic dynamic programming (DP). Furthermore, the long-term stochastic uncertainties were modeled based on the Markov chain process. The long-term optimal investment strategies were then solved for combined wind-thermal investors based on the semi-definite programming (SDP) technique. Finally, the proposed framework was implemented in the hypothetical restructured power market using the IEEE reliability test system (RTS). The conducted case study confirmed that this framework provides robust decisions and precise information about the restructured power market for combined wind-thermal investors.

Energy efficiency (EE) level has become an essential environmental index of products and can be improved by EE innovation. With consideration of EE level evolution and market differentiation, an optimal control model under a two-market framework is proposed to investigate EE innovation and two-stage pricing strategies. Impacts of consumer environmental awareness (CEA) and EE standard on optimal investment and pricing strategies are discussed. Results indicate that environmental awareness and standard result in strategy shift. As environmental awareness increases, the EE level driven by investment strategy may switch from staying in traditional market, to expanding markets by entering the green market and remaining at the standard, till capturing the green market and keeping above that standard. Impacts of standard on strategy shift exhibit a tricky trend. For loose and appropriate standards, the producer prefers to invest more to expand market by entering the green market with the increase of standard. However, a stringent standard may prevent the producer from entering the green market. In addition, optimal prices in both stages are positively impacted by the CEA and the standard.

This work considers optimal investment and reinsurance strategies for an insurer with stochastic economic factor. In our mathematical model, a risk-free asset and a risky asset are assumed to rely on a stochastic economic factor which is described by a diffusion process. We generalize the claim process to a compound Poisson process with the stochastic economic factor. Using expected utility maximization, we characterize the optimal strategy of investment-reinsurance under the power utility function. We use dynamic programming principle to derive the Hamilton–Jacobi–Bellman (HJB) equation. Then, by analysing the solution of the HJB equation, the optimal investment-reinsurance strategy is obtained and given in the verification theorem. Finally, sensitivity analysis is given to show the economic behavior of the optimal investment and reinsurance strategies.

<p style='text-indent:20px;'>In this study, under the criterion of maximizing the expected exponential utility of terminal wealth, the optimal proportional reinsurance and investment strategy for an insurer is examined with the compound Poisson claim process. To make the model more realistic, the price process of the risky asset is modelled by the Brownian motion risk model with dividends and transaction costs, where the instantaneous of investment return follows as a mean-reverting Ornstein-Uhlenbeck process. At the same time, the net profit condition and variance reinsurance premium principle are also considered. Using stochastic control theory, explicit expressions for the optimal policy and value function are derived, and various numerical examples are given to further demonstrate the effectiveness of the model.</p>

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

The aim of this paper is to develop an optimal long-term bond investment strategy which can be applied to real market situations. This paper employs Merton's intertemporal framework to accommodate the features of a stochastic interest rate and the time-varying dynamics of bond returns. The long-term investors encounter a partial information problem where they can only observe the market bond prices but not the driving factors of the variability of the interest rate and the bond return dynamics. With the assumption of Gaussian factor dynamics, we are able to develop an analytical solution for the optimal long-term investment strategies under the case of full information. To apply the best theoretical investment strategy to the real market we need to be aware of the existence of measurement errors representing the gap between theoretical and empirical models. We estimate the model based on data for the German securities market and then the estimation results are employed to develop long-term bond investment strategies. Because of the presence of measurement errors, we provide a simulation study to examine the performance of the best theoretical investment strategy. We find that the measurement errors have a great impact on the optimality of the investment strategies and that under certain circumstance the best theoretical investment strategies may not perform so well in a real market situation. In the simulation study, we also investigate the role of information about the variability of the stochastic interest rate and the bond return dynamics. Our results show that this information can indeed be used to advantage in making sensible long-term investment decisions.

Empirically 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.

Inconsistent Investment and Consumption Problems

Optimal investment management for a defined contribution pension fund under imperfect information

In order to achieve the hydrogen economy and respond to initial hydrogen demand appropriately, a hydrogen production and operation methodology is required to secure the economic feasibility of long‐term on‐site HRS. This study proposes a novel investment strategy for on‐site hydrogen production to meet future hydrogen demand. The optimal investment strategy based on the dual‐modal mode of combined autothermal reforming (ATR) and steam methane reforming (SMR) is proposed for hydrogen production using natural gas (NG) as a raw material. To predict hydrogen demand from 2020 to 2030, the machine learning (ML) technique was adopted. R2 and MSE as result using ML were 0.9936 and 6.88 × 10−5, respectively. In addition, the ATR‐SMR hydrogen strategy (ASHS) process was analyzed and compared with the SMR‐SMR and ATR‐ATR hydrogen strategy (SSHS and AAHS) processes in terms of optimal operation rate, storage tank management, economics, and environmental impacts. The operation rate of proposed hydrogen production processes was determined by the hydrogen demand and storage tank level, and the optimal investment plan to install additional hydrogen process depends on the total amount of hydrogen production. In this study, these results were observed due to the effective combination of the strengths of ATR and SMR. Consequently, the ASHS had the best cost‐effectiveness (LCOH at $5.63/kg H2) and environmental friendliness (unit CO2eq emissions at 10.21 kg CO2eq/kg H2 and 1.73 kg CO2eq/kg H2 with CCS). This study includes sensitivity analysis and a comparison of CO2 taxes by the country for three proposed hydrogen production processes. It could contribute to the optimal operation of the on‐site hydrogen production system in preparation for future hydrogen demand.