Inconsistent Investment and Consumption Problems

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

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.

This paper studies the optimal investment and consumption strategies in a two-asset model. A dynamic Value-at-Risk constraint is imposed to manage the wealth process. By using Value at Risk as the risk measure during the investment horizon, the decision maker can dynamically monitor the exposed risk and quantify the maximum expected loss over a finite horizon period at a given confidence level. In addition, the decision maker has to filter the key economic factors to make decisions. Considering the cost of filtering the factors, the decision maker aims to maximize the utility of consumption in a finite horizon. By using the Kalman filter, a partially observed system is converted to a completely observed one. However, due to the cost of information processing, the decision maker fails to process the information in an arbitrarily rational manner and can only make decisions on the basis of the limited observed signals. A genetic algorithm was developed to find the optimal investment, consumption strategies, and observation strength. Numerical simulation results are provided to illustrate the performance of the algorithm.

We analyse an optimal portfolio and consumption problem with stochastic factor and delay over a finite time horizon. The financial market includes a risk-free asset, a risky asset and a stochastic factor. The price process of the risky asset is modelled as a stochastic differential delay equation whose coefficients vary according to the stochastic factor; the drift also depends on its historical performance. Employing the stochastic dynamic programming approach, we establish the associated Hamilton–Jacobi–Bellman equation. Then we solve the optimal investment and consumption strategies for the power utility function. We also consider a special case in which the price process of the stochastic factor degenerates into a Cox–Ingersoll–Ross model. Finally, the effects of the delay variable on the optimal strategies are discussed and some numerical examples are presented to illustrate the results. doi:10.1017/S1446181119000014

Optimal consumption and investment strategies with stochastic interest rates

This paper studies an optimal consumption and portfolio choice problem for unemployed people who have an option to work. Our problem is to find optimal consumption, risky investment, and workforce re-entry strategies for the unemployed. We find a closed form of the critical wealth level to re-enter the workforce. We show that the unemployed with a higher disutility of labor or a larger relative risk aversion are more reluctant to re-enter the workforce.

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

Optimal consumption and investment strategies with a perishable and an indivisible durable consumption good

Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting

Optimal Consumption and Investment Strategies with a Perishable and an Indivisible Durable Consumption Good

The question how to optimize consumption and portfolio choice over the life cycle has been widely discussed in the literature so far. In this paper we concentrate on a retiree's optimal consumption and portfolio selection over his remaining years of life. We apply the logistic model of mortality thus modeling the empirically observed increase of mortality during the retirement period. The optimal consumption strategy and portfolio choice are established by reducing the Hamilton-Jacobi-Bellmann equation to the explicit solution of an ordinary differential function (ODF) that includes the mortality rate. A general finding is that the Merton-Samuelson result of constant portfolio choice for a constant mortality is confirmed for arbitrary mortality. The portfolio choice is only influenced by risk and return of assets and the retirees’ risk aversion. To get the specific optimal consumption strategy in a realistic situation the logistic model of mortality has been fitted to the data of the Statistical Yearbook for the Federal Republic of Germany 2006/2008. The optimal initial value for the ODF is obtained by numerical methods. The solution provides a large increase in the ratio of optimal consumption to wealth up to about 92 years followed by a sharp decrease. A bequest motive dampens the magnitudes of the ups and downs of the consumption ratio but does not change the basic shape.

With the rapid development of smart grid technology, load regulation on the demand side has become a flexible approach for load peak shaving and renewable energy accommodation. In this paper, an optimal wind power consumption strategy is proposed based on the time series analysis of electricity load. In view of the periodicity of residential load on both working days and non-working days, the double seasonal ARIMA model is applied to predict users' behavior and the adjustable electricity load for wind power consumption. In addition, the difference between residential load and wind power generation is taken as the objective function for optimal power consumption. The problem of wind energy consumption is solved by prioritizing residential load according to the correlation between the load series and wind power series in each time slot. Experimental results demonstrated the reliability and accuracy of the proposed algorithm.

Many firms have stockholders who face severe restrictions on their ability to sell their shares and diversify the risk of their personal wealth. We study the costs of these liquidity restrictions on stockholders using a continuous-time portfolio choice framework. These restrictions have major effects on the optimal investment and consumption strategies because of the need to hedge the illiquid stock position and smooth consumption in anticipation of the eventual lapse of the restrictions. These results provide a number of important insights about the effects of illiquidity in financial markets.

Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity

This paper investigates the optimal consumption, investment and insurance strategies for a wage earner operating within an inflationary environment and subject to time-varying consumption constraints over a finite, continuous time horizon. We assume the financial market comprises a risk-free asset, a stock, and an index bond, with the wage earner's preference represented by the Constant Relative Risk Aversion (CRRA) utility function. The primary objective of the wage earner is to devise an optimal strategy for consumption, investment, and insurance allocation, aimed at maximizing the expected discounted utilities. By employing the martingale duality method and Feynman-Kac formula, we derive the partial differential equations governing the dual value function in the context of the Cauchy problem. Subsequently, we obtain the specific expression of the dual value function and the optimal strategies by employing integral transform methods. The impact of various model parameters on optimal strategies is further elucidated through numerical simulations, utilizing predefined parameter values.