Optimal Consumption Rate Research Articles

Singular recursive utility

We introduce the concept of singular recursive utility. This leads to a kind of singular backward stochastic differential equation (BSDE) which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular recursive utility. We derive sufficient and necessary maximum principles for this problem, and connect it to the Skorohod reflection problem. Finally, we apply our results to a specific cash flow. In this case, we find that the optimal consumption rate is given by the solution to the corresponding Skorohod reflection problem.

Retirement Spending and Biological Age

We solve a retirement lifecycle model in which the consumer's age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate in chronological age, which one can think of as working with a clock that occasionally moves backwards in time. Our paper is inspired by the growing body of medical literature that has identified biomarkers of aging which -- practically speaking -- offer better estimates of expected remaining lifetime and future mortality rates. It isn't farfetched to argue that in the not-too-distant future of wearable technology, personal age will be more closely associated with biological time vs. calendar age or time. Thus, after introducing our stochastic mortality model we derive optimal consumption rates in a classic Yaari (1965) framework adjusted to our proper clock and time. In addition to the normative implications of having access to biological age, our positive objective is to partially explain the cross-sectional heterogeneity in retirement spending rates at any given chronological age. In sum, we argue that biological age is not a sufficient statistic for making economic decisions and you need information about both your ages to behave rationally.

A Spatio-temporal incentive scheme with consumer demand awareness for participatory sensing

Participatory sensing involves smartphone users contributing data to form a body of knowledge. This paper first develops the concept of quality of contribution and consumption in the spatio-temporal sense for participatory sensing. Recognising that a significant issue which determines the success of participatory sensing is the incentive for contributors, we propose a spatio-temporal incentive (STI) scheme with consumer demand awareness. The STI scheme considers the spatio-temporal relevance between contributors and consumers and incentivizes contributors to contribute according to consumer demand. Only spatio-temporal relevant contributors for enquiry-based consumption and a subset of contributors which provide sufficient sensing coverage for coverage-based consumption are remunerated, which lead to a targeted and economical incentive scheme. Following the STI scheme, contributors and consumers determine their participation levels to maximize their utilities, and a resulting market equilibrium can be achieved, where the optimal contribution level and the optimal consumption rate, respectively, are employed. A closed form expression for the quality of consumption at the market equilibrium is derived. The performance of the STI scheme is investigated through extensive simulations, which show that good quality of consumption and sensing coverage can be experienced by consumers.

Maximum principle for optimal control of anticipated forward–backward stochastic differential delayed systems with regime switching

SummaryThis paper is concerned with a Pontryagin maximum principle for optimal control problem of stochastic system, which is described by an anticipated forward–backward stochastic differential delayed equation and modulated by a continuous‐time finite‐state Markov chain. We establish a necessary maximum principle and sufficient verification theorem for the optimal control by virtue of the duality method and convex analysis. To illustrate the theoretical results, we apply them to a recursive utility investment‐consumption problem, and the optimal consumption rate is derived explicitly. Copyright © 2015 John Wiley & Sons, Ltd.

Optimal control for stochastic differential delay equations with Poisson jumps and applications

Abstract This paper is concerned with the optimal control problem for stochastic differential delay equations with Poisson jumps, in which both state and control delays are involved. We obtain the necessary and sufficient maximum principles for the optimal control by virtue of the duality method and the anticipated backward stochastic differential equations with Poisson jumps. An optimal consumption rate problem is discussed to illustrate the applications of our results.

Verification Theorem Of Stochastic Optimal Control With Mixed Delay And Applications To Finance

AbstractThis paper focuses on a general model of a controlled stochastic differential equation with mixed delay in the state variable. Based on the Itô formula, stochastic analysis, convex analysis, and inequality technique, we obtain a semi‐coupled forward‐backward stochastic differential equation with mixed delay and mixed initial‐terminal conditions and prove that such forward‐backward system admits a unique adapted solution. The verification theorem for an optimal control of a system with mixed delay is established. The obtained results generalize and improve some recent results, and they are more easily verified and applied in practice. As an application, we conclude with finding explicitly the optimal consumption rate from the wealth process of a person given by a stochastic differential equation with mixed delay which fit into our general model.

H–J–B Equations of Optimal Consumption-Investment and Verification Theorems

We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H---J---B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings.

Optimal consumption problems in discontinuous markets

We study an extension of Merton’s classical portfolio investment – consumption optimization problem (1969–1970) to a particular case of complete discontinuous market, with a single jump. The market consists of a non-risky asset, a ‘standard risky’ asset and a risky asset with discontinuous price dynamics (e.g. a defaultable bond or a mortality linked security). We consider three different problems of maximization of the expected utility from consumption: in the case when the investment horizon is fixed and finite, when it is finite, but possibly uncertain and when it is infinite. The innovative setting is the second one. In a general stochastic coefficients’ model, we solve the problems and we compare the three optimal consumption rates, finding quite interesting results. In the logarithmic and power utility cases, explicit solutions are provided. Furthermore, the benchmark – constant coefficients’ case is deeply investigated and a partial information setting is also studied in the uncertain time horizon case.

On Investment Consumption Modeling with Jump Process Extensions for Productive Sectors

We consider the optimal investment and consumption behavior of an agricultural sector that generates income from productive capital and interest payments and that has expenditures due to interest payments for debt. The productivity of capital, the interest rate, and the capital depreciation rate are uncertain. We adapt an existing model from the literature and generalize it to a stochastic depreciation of capital stock. Moreover, we assume a discontinuous evolution of the productivity of capital. The uncertainties are modeled as stochastic processes with discontinuous paths using well-known Wiener processes and simple Poisson processes. Accordingly, the investor's net wealth follows a jump diffusion stochastic differential equation. The goal of maximizing the utility of consumption over an infinite time horizon leads to a stochastic optimal control problem. We choose a hyperbolic absolute risk aversion utility function. To determine the optimal investment and consumption rate, the associated Hamilton---Jacobi---Bellman equation is solved by a separation method, and a verification theorem is applied.

Application and optimisation studies of a zinc electrowinning process simulation

AbstractUsing existing models, a zinc electrowinning cell house was simulated including electrowinning cells, electrolyte storage, and cooling towers. Optimisations and applications of the simulation were investigated as applicable to a cell house. Conditions were identified for achieving optimal current efficiency, energy consumption, and zinc production rate for a single cell and the entire cell house. The minimal energy consumption of the cell house was found to be larger than single cells primarily due to the lack of available control of the acid concentration. Water loss through cooling towers and the movement of a well‐mixed non‐interacting impurity was also tracked.

THE EFFECT OF INFLATION RISK AND SUBSISTENCE CONSTRAINTS ON PORTFOLIO CHOICE

The optimal portfolio selection problem under inflation risk and subsistence constraints is considered. There are index bonds to invest in financial market and it helps to hedge the inflation risk. By applying the martingale method, the optimal consumption rate and the optimal portfolios are obtained explicitly. Furthermore, the quantitative effect of inflation risk and subsistence constraints on the optimal polices are also described.

PORTFOLIO CHOICE UNDER INFLATION RISK: MARTINGALE APPROACH

The optimal portfolio selection problem under inflation risk is considered in this paper. There are three assets the economic agent can invest, which are a risk free bond, an index bond and a risky asset. By applying the martingale method, the optimal consumption rate and the optimal portfolios for each asset are obtained explicitly.

A Maximum Principle for Infinite Horizon Delay Equations

We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our results with an application to the optimal consumption rate from an economic quantity.

Backward stochastic differential equations with respect to general filtrations and applications to insider finance

In this paper, we study backward stochastic dierential equations with respect to general filtrations. The results are used to find the optimal consumption rate for an insider from a cash

Pricing Electricity Derivatives under Future Information

In this article we derive risk-neutral option price formulas for both plain-vanilla and exotic electricity futures derivatives on the basis of diverse arithmetic multi-factor Ornstein-Uhlenbeck spot price models admitting seasonality, while – in order to avoid “information miss-specification” – we take additional forward-looking knowledge on future price behavior into account via tailor-made enlargements of the underlying historical information filtrations. In this insider trading context, we also correlate electricity prices with outdoor temperature and treat a related pricing problem under supplementary temperature forecasts. Meanwhile, we use Fourier transform techniques and results from complex analysis to handle the emerging anticipating conditional expectations. As a by-product we derive related risk and information premia. Finally, we investigate utility-maximizing portfolio selection and optimal consumption rates in electricity futures markets even under forward-looking information.

Multiple equilibria and indifference-threshold points in a rational addiction model

Becker and Murphy (J Polit Econ 96(4):675–700, 1988) have established the existence of unstable steady states leading to threshold behavior for optimal consumption rates in intertemporal rational addiction models. In the present paper a simple linear-quadratic optimal control model is used to illustrate how their approach fits into the framework of multiple equilibria and indifference-threshold points. By changing the degree of addiction and the level of harmfulness we obtain a variety of behavioral patterns. In particular we show that when the good is harmful as well as very addictive, an indifference-threshold point, also known in the literature as a Skiba point, separates patterns converging to either zero or maximal consumption, where the latter occurs in the case of a high level of past consumption. This implicitly shows that an individual needs to be aware in time of these characteristics of the good. Otherwise, he/she may start consuming so much that in the end he/she is totally addicted.

Optimal retirement consumption with a stochastic force of mortality

We extend the lifecycle model (LCM) of consumption over a random horizon (also known as the Yaari model) to a world in which (i) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii) consumers can adapt their consumption strategy to new information about their mortality rate (also known as health status) as it becomes available. In particular, we derive the optimal consumption rate and focus on the impact of mortality rate uncertainty versus simple lifetime uncertainty — assuming that the actuarial survival curves are initially identical — in the retirement phase where this risk plays a greater role.In addition to deriving and numerically solving the partial differential equation (PDE) for the optimal consumption rate, our main general result is that when the utility preferences are logarithmic the initial consumption rates are identical. But, in a constant relative risk aversion (CRRA) framework in which the coefficient of relative risk aversion is greater (smaller) than one, the consumption rate is higher (lower) and a stochastic force of mortality does make a difference.That said, numerical experiments indicate that, even for non-logarithmic preferences, the stochastic mortality effect is relatively minor from the individual’s perspective. Our results should be relevant to researchers interested in calibrating the lifecycle model as well as those who provide normative guidance (also known as financial advice) to retirees.

Effect of light intensity and nitrogen starvation on CO2 fixation and lipid/carbohydrate production of an indigenous microalga Scenedesmus obliquus CNW-N

Engineering strategies were applied to improve the CO2 fixation rate and carbohydrate/lipid production of a Scenedesmus obliquus CNW-N isolate. The light intensity that promotes cell growth, carbohydrate/lipid productivity, and CO2 fixation efficiency was identified. Nitrogen starvation was also employed to trigger the accumulation of lipid and carbohydrate. The highest productivity of biomass, lipid, and carbohydrate was 840.57mgL−1d−1, 140.35mgL−1d−1. The highest lipid and carbohydrate content was 22.4% (5-day N-starvation) and 46.65% (1-day N-starvation), respectively. The optimal CO2 consumption rate was 1420.6mgL−1d−1. This performance is better than that reported in most other studies. Under nitrogen starvation, the microalgal lipid was mainly composed of C16/C18 fatty acid (around 90%), which is suitable for biodiesel synthesis. The carbohydrate present in the biomass was mainly glucose, accounting for 77–80% of total carbohydrates. This carbohydrate composition is also suitable for fermentative biofuels production (e.g., bioethanol and biobutanol).

Scenedesmus obliquus CNW-N as a potential candidate for CO2 mitigation and biodiesel production

This study aimed to achieve higher CO(2) consumption ability and lipid productivity of an indigenous microalgal isolate Scenedesmus obliquus CNW-N by a two-stage cultivation strategy. The microalga strain was first cultivated with 10% CO(2) using a nutrient-rich medium to promote cell growth, which was followed by a nutrient-deficient condition to trigger lipid accumulation. The optimal biomass productivity, lipid productivity, and CO(2) consumption rate were 292.50mgL(-1)d(-1), 78.73mgL(-1)d(-1) (38.9% lipid content per dry weight of biomass), and 549.90mgL(-1)d(-1), respectively. This performance is superior to the results from most of the related studies. Under the nutrient-deficient condition, the microalgal lipid was mainly composed of C16/C18 fatty acids (accounting for 89% of total fatty acids), which is suitable for biodiesel synthesis.

Maximum principle for the stochastic optimal control problem with delay and application

In this paper, we consider an optimal control problem for the stochastic system described by stochastic differential equations with delay. We obtain the maximum principle for the optimal control of this problem by virtue of the duality method and the anticipated backward stochastic differential equations. Our results can be applied to a production and consumption choice problem. The explicit optimal consumption rate is obtained.