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.

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.

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 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 Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with Jump-Diffusion Process

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Hanlei Hu ◽  
Zheng Yin ◽  
Xiujuan Gao
Keyword(s):  
Diffusion Process ◽  
Optimal Strategies ◽  
Jump Diffusion ◽  
Sensitivity Analyses ◽  
Programming Approach ◽  
Investment Strategies ◽  
Optimal Reinsurance ◽  
Bellman Equations ◽  
Dynamic Programming Approach ◽  
Jump Diffusion Process

The optimal reinsurance-investment strategies considering the interests of both the insurer and reinsurer are investigated. The surplus process is assumed to follow a jump-diffusion process and the insurer is permitted to purchase proportional reinsurance from the reinsurer. Applying dynamic programming approach and dual theory, the corresponding Hamilton-Jacobi-Bellman equations are derived and the optimal strategies for exponential utility function are obtained. In addition, several sensitivity analyses and numerical illustrations in the case with exponential claiming distributions are presented to analyze the effects of parameters about the optimal strategies.

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 Valuation of Swing Options under a Regime-Switching Mean-Reverting Model

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Lingjie Shao ◽  
Kaili Xiang
Keyword(s):  
Electricity Market ◽  
Regime Switching ◽  
Seasonal Pattern ◽  
Market Price ◽  
Spot Price ◽  
Programming Approach ◽  
Volume Constraint ◽  
Uhlenbeck Process ◽  
Swing Options ◽  
Ornstein Uhlenbeck Process

In this paper, we study the valuation of swing options on electricity in a model where the underlying spot price is set to be the product of a deterministic seasonal pattern and Ornstein-Uhlenbeck process with Markov-modulated parameters. Under this setting, the difficulties of pricing swing options come from the various constraints embedded in contracts, e.g., the total number of rights constraint, the refraction time constraint, the local volume constraint, and the global volume constraint. Here we propose a framework for the valuation of the swing option on the condition that all the above constraints are nontrivial. To be specific, we formulate the pricing problem as an optimal stochastic control problem, which can be solved by the trinomial forest dynamic programming approach. Besides, empirical analysis is carried out on the model. We collect historical data in Nord Pool electricity market, extract the seasonal pattern, calibrate the Ornstein-Uhlenbeck process parameters in each regime, and also get market price of risk. Finally, on the basis of calibration results, a specific numerical example concerning all typical constraints is presented to demonstrate the valuation procedure.

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