Robust optimal asset-liability management with penalization on ambiguity

The aim of this study is to estimate the optimal forest harvest considering economic and environmental objectives in an uneven-aged forest in the north of Iran. Required data were collected such as stumpage price, harvesting variable costs, growth, volume, basal area, sequestrated carbon, carbon dioxide storage, and price. The required input models for optimization were estimated using the collected data. A stochastic dynamic programming technique was used for optimization. The results indicated that the harvesting volume was higher when only the economic objective was considered instead of considering economic and environmental objectives. The results also indicated that the harvesting volume would occur at a higher level of volume per hectare if we only consider the environmental objective. The results showed that the expected present value was higher when economic and environmental objectives were considered simultaneously. The results indicated when interest rate increased, the harvesting time and the expected present value decreased. The results showed that the expected present value increases with increasing the risk. The results of this study can be a guideline for optimal forest management.

In this paper, we investigate the impacts of model misspecification on the insurer’s investment behaviours. Model misspecification comes from either the financial market or insurance business due to economic fluctuation. From the risk control point of view, we assume that an insurer has ambiguity aversion and we study the robust optimal investment strategy for the insurer under several settings. As a benchmark, we firstly obtain the optimal investment strategy for the insurer without considering model misspecification. Then, by assuming that model misspecification only exists in the financial market, we obtained the robust optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation under the objective of minimizing the probability of ruin. The results tells us the insurer’s ambiguity aversion leads to a more conservative investment behaviour. At last, we incorporate the model misspecification for both financial market and insurance business in a general framework. The robust optimal investment is also obtained and we find that the investment is enlarged due to the insurer’s ambiguity aversion on the insurance business because of the motivation of ambiguity hedging. The numerical examples display that different ambiguity aversion level on the financial market and insurance business have different impacts on the robust investment strategy.

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.

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

A stochastic dynamic programming approach for delay management of a single train line

This paper presents a novel formulation for integrated bidding and hydrothermal scheduling, where the market clearing price (MCP) is modeled as a Markov chain and the risks are directly formulated in the objective function in terms of MCP variances. The self-scheduling requirements and interactions between the energy and reserve markets are considered. A Lagrangian relaxation based algorithm is then developed to solve this problem, and a stochastic dynamic programming approach is developed to solve the unit subproblems. Since the bidding of pumped-storage units plays important roles in both the energy and reserve markets, and significantly affects thermal biddings, it is the focus in this paper. Effects of self-scheduling constraints, risk management and reserve market on the energy bidding strategies are analyzed. Numerical testing based on an 11-unit system in New England shows that the method can generate energy and reserve bid curves in 4-5 minutes, and risks of buying power at high market price are effectively reduced.

Joint production and maintenance optimization in flexible hybrid Manufacturing–Remanufacturing systems under age-dependent deterioration

In this paper, we consider a single item single level production planning problem with uncertain and dynamic demand. The uncertainties are modelled through the probability density function of the demand. The system is studied in a rolling-horizon framework, in which data is updated at each iteration and makes the demand non-stationary. In this context, we model a cost minimization problem using a stochastic dynamic programming approach, which allows to integrate the update of the demand density into the optimization process. We calculate the optimal production quantities in a specific case where linear regression is the forecasting method used and the production lead-time is equal to one period. We finally run a simulation to illustrate the optimality of the solution, and to show its efficiency compared to others classical production planning procedures.

ABSTRACTPerformance measures are often outlined in the section of the service‐level agreement (SLA) of the contract between a supplier and a retailer. They are monitored periodically, and penalty and/or bonus payments are imposed in each performance review period, according to the SLA clauses. Previous studies have mostly considered a static inventory policy in analyzing SLAs. However, in practice, the supplier may have an opportunity to adjust the stock level in each inventory review period, according to the observed performance. This study analyzes the dynamic stocking decision for a supplier facing an SLA where the supplier sells a single product to the retailer. The ready rate is used to measure the performance in an SLA. To this end, models for both lump‐sum and linear penalty/bonus structures are developed, and the optimal stocking decisions for a strategic supplier are calculated using the stochastic dynamic programming approach. The results are then compared with the optimal static inventory policy, and new insights are derived to efficiently design an inventory system for the suppliers that are subject to service‐level incentives. In addition, we investigate the impact of SLA parameters—such as the length of the performance review period and incentive structures—on a supplier's performance, with the probability of meeting or exceeding the target service levels and the supplier's cost. We also consider the impact of demand distribution and inventory holding costs. Results show that under lump‐sum incentives, a longer performance review period benefits both the supplier and the buyer, given that the average ready rate increases with less variability as the length of the performance review period increases, leading to decrements in the supplier's total costs. In this scenario, there is a higher chance of gaining bonuses/avoiding penalties for a strategic supplier who adopts a dynamic inventory policy. On the other hand, under linear incentives, the impact of the performance review period on the supplier's cost and the performance measure (i.e., ready rate) is complicated and depends on the magnitude of the holding cost and the bonus and/or penalty structure of the contract. Under this scheme, the performance of a static inventory policy is highly dependent on the holding cost because a high holding cost may lead to failure to meet the contract requirements in terms of the service level.

We present strategies for decision making under uncertainty and adversary action modeling for small UAV operations. Uncertainty comes from the stochastic nature of the environment and from incomplete knowledge of adversary actions/behaviors. A stochastic dynamic programming approach is used to optimize (continuous) resource allocation (fuel reserves) in the face of uncertainty. Different scenarios for adversary responses are considered and analyzed in simulation.

In this study, a microgrid with storage (battery, hot water tank) and solar panel is considered. We benchmark two algorithms, MPC and SDDP, that yield online policies to manage the microgrid, and compare them with a rule based policy. Model Predictive Control (MPC) is a well-known algorithm which models the future uncertainties with a deterministic forecast. By contrast, Stochastic Dual Dynamic Programming (SDDP) models the future uncertainties as stagewise independent random variables with known probability distributions. We present a scheme, based on out-of-sample validation, to fairly compare the two online policies yielded by MPC and SDDP. Our numerical studies put to light that MPC and SDDP achieve significant gains compared to the rule based policy, and that SDDP overperforms MPC not only on average but on most of the out-of-sample assessment scenarios.

Risk-averse stochastic dual dynamic programming approach for the operation of a hydro-dominated power system in the presence of wind uncertainty

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

The least squares Monte Carlo method is a decision evaluation method that can capture the effect of uncertainty and the value of flexibility of a process. The method is a stochastic approximate dynamic programming approach to decision making. It is based on a forward simulation coupled with a recursive algorithm which produces the near-optimal policy. It relies on the Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the least squares Monte Carlo method by improving the sampling method used to generate the technical uncertainties used in obtaining the production profiles. The probabilistic collocation method has been proven to be a robust and efficient uncertainty quantification method. By using the sampling methods of the probabilistic collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision evaluation method. Thus, we introduce the least squares probabilistic collocation method. The decision evaluation considered a number of technical and economic uncertainties. Three reservoir case studies were used: a simple homogeneous model, the PUNQ-S3 model, and a modified portion of the SPE10 model. The results show that using the sampling techniques of the probabilistic collocation method produced relatively accurate responses compared with the original method. Different possible enhancements were discussed in order to practically adapt the least squares probabilistic collocation method to more realistic and complex reservoir models. Furthermore, it is desired to perform the method to evaluate high-dimensional decision scenarios for different chemical enhanced oil recovery processes using real reservoir data.

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