scholarly journals Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2053
Author(s):  
M’hamed Gaïgi ◽  
Idris Kharroubi ◽  
Thomas Lim
Keyword(s):  
Differential Equation ◽  
Natural Resource ◽  
Market Price ◽  
Programming Approach ◽  
Infinite Time ◽  
Delay Constraints ◽  
Dynamic Programming Approach ◽  
Brownian Process ◽  
Renewable Natural Resource ◽  
The Value Function

In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and sell it at a stochastic market price modeled by a geometric Brownian process. We assume that there are delay constraints imposed on the decisions of the manager. More precisely, starting harvesting order and selling order are executed after a delay. By using the dynamic programming approach, we characterize the value function as the unique solution to an original partial differential equation. We complete our study with some numerical illustrations.

scholarly journals A Bilevel Stochastic Dynamic Programming Model to Assess the Value of Information on Actual Food Quality at Wholesale Markets

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Xiangyu Hou ◽  
Rene Haijema ◽  
Dacheng Liu
Keyword(s):  
Dynamic Programming ◽  
Programming Model ◽  
Market Price ◽  
Programming Approach ◽  
Stochastic Dynamic ◽  
Wholesale Market ◽  
Dynamic Programming Approach ◽  
Additional Information ◽  
Similar Appearance ◽  
Inventory Decision

In the fresh produce wholesale market, the market price is determined by the total demand and supply. The price is stochastic, and either wholesaler or retailer has few influence on it. In the wholesaler’s inventory decision, the price’s uncertainty plays an important role as well as the uncertainty from the demand side: the wholesaler makes his decision based on the retailer’s ordering, which is influenced by the stochastic market price and the distribution of the consumer’s demand. In addition, when at the wholesale stage, the products show a similar quality of similar appearance. With more efforts being input, the wholesaler could detect and record more additional information than that reflected from the appearance. Based on this, he can classify the quality into different levels. No experience shows how the wholesaler could use the underlying quality information and how much this information could improve his profit. To describe and explore this problem, a bilevel dynamic programming approach is employed. We evaluate different strategies of using the underlying information, show the features of the optimal policy, develop heuristics, and discuss the influence of factors such as quality and market price. We also develop the managerial principles for the practical use.

scholarly journals The Rayleigh quotient and dynamic programming

1978 ◽  
Vol 1 (4) ◽  
pp. 401-405
Author(s):  
Richard Bellman
Keyword(s):  
Differential Equation ◽  
Dynamic Programming ◽  
Nonlinear Partial Differential Equation ◽  
Rayleigh Quotient ◽  
Programming Approach ◽  
Nonlinear Characteristic ◽  
Dynamic Programming Approach ◽  
Computational Aspects ◽  
Characteristic Values ◽  
Matrix Problems

The purpose of this paper is to derive a nonlinear partial differential equation for whichλgiven by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation.

scholarly journals A multi-period risk sharing supply chain contract under consideration of price and demand uncertainties

2021 ◽  
Author(s):  
Isil Tari
Keyword(s):  
Exchange Rate ◽  
Regime Switching ◽  
Risk Sharing ◽  
Market Price ◽  
Sensitivity Analyses ◽  
Programming Approach ◽  
Random Demand ◽  
Supply Contract ◽  
Dynamic Programming Approach ◽  
Markovian Regime Switching

Exchange rate is extremely volatile and displays a Markovian regime switching property. This report proposes a multi-period procurement problem with a flexible quantity risk-sharing supply contract that may provide a prevention against exchange rate (FX) fluctuations for international traders. The buyer assumed to be encountered with a random price modelled by a regime-switching geometric Brownian motion and also random demand. The proposed risk sharing supply contract model helps to compensate supplier for the depreciating market price and also helps buyer when purchase price increases. According to the author’s knowledge, none of the studies in the literature considers a risk-sharing supply contract with random demand and random price while modelling the exchange rates by regime switching approach. Multi-period lattice model is developed for valuation of risk-sharing supply contract. The problem is solved with using dynamic programming approach. A numerical example and sensitivity analyses are presented to illustrate the proposed model.

Stochastic and Fuzzy Decision Problems in Three-Workpiece Lapping Process

1981 ◽  
Vol 103 (2) ◽  
pp. 192-196
Author(s):  
Y. Sakai ◽  
Y. Tanaka ◽  
M. Ido
Keyword(s):  
Differential Equation ◽  
Dynamic Programming ◽  
Stochastic Differential Equation ◽  
Decision Problems ◽  
Programming Approach ◽  
Fuzzy Decision ◽  
Flat Surfaces ◽  
Dynamic Programming Approach ◽  
Process Dynamics ◽  
Optimal Policies

The basic, remarkable properties lying in the three-workpiece lapping process were previously described by the authors. It was assured there that highly flat surfaces can be obtained predicting and controlling the change in shape of the three workpieces. A methodology of an optimal handling of the process was also developed in another paper, regarding the process as a deterministic one. A modified but more practical discussion is taken up here taking into consideration the stochastic behavior of the process. In so doing, a stochastic treatment in the dynamic programming approach is introduced with the reformulation of the process dynamics as a stochastic differential equation. The concept of fuzzy sets is also employed in order to overcome the difficulty in setting the criterion for optimal policies, which seems to be useful in manufacturing fields.

scholarly journals A multi-period risk sharing supply chain contract under consideration of price and demand uncertainties

2021 ◽  
Author(s):  
Isil Tari
Keyword(s):  
Exchange Rate ◽  
Regime Switching ◽  
Risk Sharing ◽  
Market Price ◽  
Sensitivity Analyses ◽  
Programming Approach ◽  
Random Demand ◽  
Supply Contract ◽  
Dynamic Programming Approach ◽  
Markovian Regime Switching

Exchange rate is extremely volatile and displays a Markovian regime switching property. This report proposes a multi-period procurement problem with a flexible quantity risk-sharing supply contract that may provide a prevention against exchange rate (FX) fluctuations for international traders. The buyer assumed to be encountered with a random price modelled by a regime-switching geometric Brownian motion and also random demand. The proposed risk sharing supply contract model helps to compensate supplier for the depreciating market price and also helps buyer when purchase price increases. According to the author’s knowledge, none of the studies in the literature considers a risk-sharing supply contract with random demand and random price while modelling the exchange rates by regime switching approach. Multi-period lattice model is developed for valuation of risk-sharing supply contract. The problem is solved with using dynamic programming approach. A numerical example and sensitivity analyses are presented to illustrate the proposed model.

PRICING AND CALIBRATION OF A CHOOSER FLEXIBLE CAP

2010 ◽  
Vol 27 (02) ◽  
pp. 243-256 ◽  
Author(s):  
DAISUKE ITO ◽  
MASAMITSU OHNISHI ◽  
YASUHIRO TAMBA
Keyword(s):  
Dynamic Programming ◽  
Yield Curve ◽  
Market Price ◽  
Programming Approach ◽  
No Arbitrage ◽  
Dynamic Programming Approach ◽  
Price Data ◽  
Initial Yield ◽  
Pricing Problems ◽  
Interim Period

In this paper, we deal with no-arbitrage pricing problems of a chooser flexible cap written on an underlying LIBOR. The chooser flexible cap allows a right for a buyer to exercise a limited and pre-determined number of the interim period caplets in a multiple-period cap agreement. Assuming a common diffusion short rate dynamics, e.g., Hull–White model, we propose a dynamic programming approach for their risk neutral evaluation. This framework is suited to a calibration from an observed initial yield curve and market price data of discount bonds, caplets, and floorlets.

scholarly journals Backward stochastic PDEs related to the utility maximization problem

2010 ◽  
Vol 17 (4) ◽  
pp. 705-740
Author(s):  
Michael Mania ◽  
Revaz Tevzadze
Keyword(s):  
Differential Equation ◽  
Utility Maximization ◽  
Market Model ◽  
Maximization Problem ◽  
Programming Approach ◽  
Stochastic Pdes ◽  
Dynamic Programming Approach ◽  
General Utility ◽  
Continuous Semimartingale ◽  
Utility Maximization Problem

Abstract We study utility maximization problem for general utility functions using the dynamic programming approach. An incomplete financial market model is considered, where the dynamics of asset prices is described by an -valued continuous semimartingale. Under some regularity assumptions, we derive the backward stochastic partial differential equation related directly to the primal problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward stochastic differential equation. The cases of power, exponential and logarithmic utilities are considered as examples.

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