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Principal-Multiagents problem under equivalent changes of measure: General study and an existence result

STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2024年 177卷

作者： Hernandez-Santibanez, Nicolas Univ Tecn Federico Santa Maria Dept Matemat Valparaiso Chile

We study a general contracting problem between the principal and a finite set of competitive agents, who perform equivalent changes of measure by controlling the drift of the output process and the compensator of its associated jump measure. In this setting, we generalize the dynamic programming approach developed by Cvitani & cacute;et al. (2018) and we also relax their assumptions. We prove that the problem of the principal can be reformulated as a standard stochastic control problem in which she controls the continuation utility (or certainty equivalent) processes of the agents. Our assumptions and conditions on the admissible contracts are minimal to make our approach work. We review part of the literature and give examples on how they are usually satisfied. We also present a smoothness result for the value function of a risk-neutral principal when the agents have exponential utility functions. This leads, under some additional assumptions, to the existence of an optimal contract.

关键词： Moral hazard Principal-Multiagents dynamic programming approach BSDEs with jumps PIDEs Regularity of the value function

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A condition-based maintenance policy with non-periodic inspection for k-out-of-n: G systems

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2024年 241卷

作者： Liu, Yongchao Wang, Guanjun Liu, Peng Southeast Univ Sch Math Nanjing 210096 Peoples R China

This paper studies a condition-based maintenance policy for k-out-of-n: G systems subject to economic dependence. All components in the system are identical and unrepairable, with an exponential lifetime distribution. The state of the system is not self-announcing, which can only be revealed by inspection. At each inspection moment, the maintenance decision and the next inspection plan are made according to the system status revealed by the inspection. The optimal maintenance strategy can be obtained in three steps. Firstly, a dynamic programming approach is used to determine the sequence of optimal inspection intervals gradually. Secondly, a searching method is used to optimize the preventive maintenance threshold of the system based on the renewal process theory. Thirdly, the optimal number of components that constitutes the redundant system is decided. Furthermore, the average availability and mean time to failure of the system are also derived iteratively. The effectiveness of the proposed maintenance policy is validated by a 5-out-of-n: G system. Numerical comparison with the periodic inspection policy shows the outstanding performance of the proposed maintenance policy.

关键词： Condition-based maintenance policy Economic dependence dynamic programming approach Inspection

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Optimal DC Pension Management Under Inflation Risk With Jump Diffusion Price Index and Cost of Living Process

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2022年第2期24卷 1253-1270页

作者： Zhang, Xiaoyi Hebei Univ Technol Sch Econ & Management Tianjin 300401 Peoples R China

This work deals with an optimal benefit distribution and asset allocation problem for a defined contribution (DC) pension plan during its decumulation phase. With the phenomenon of longevity, the time horizon of pension management during this phase might be long, thus the influence of inflation is considered in the context. The inflation index is subjected to a Poisson jump and a Brownian uncertainty. Motivated by the work of Wang et al. (2018), it is assumed that the scheme provides cost of living adjustment, which is extended to a jump diffusion process in this work. The plan aims to reduce fluctuations of benefit and terminal wealth by investing the fund in a financial market consisting of a bank account, an inflation indexed bond and a stock. The dynamics of two risky assets are also given by jump diffusion processes. The closed form decisions are derived by using the dynamic programming approach.

关键词： DC pension plan Inflation Poisson process Stochastic optimal control dynamic programming approach HJB equation

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Optimal Investment-Consumption and Life Insurance Strategy with Mispricing and Model Ambiguity

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2023年第3期25卷 77-77页

作者： Gu, Ailing He, Xinya Chen, Shumin Yao, Haixiang Guangdong Univ Technol Sch Math & Stat Guangzhou 510520 Peoples R China Guangdong Univ Technol Sch Management Guangzhou 510520 Peoples R China Guangdong Univ Foreign Studies Sch Finance Guangzhou 510006 Peoples R China

In this paper, we consider the optimal investment-consumption and life insurance strategy for a wage earner who has uncertain labor income described by an Ornstein-Uhlenbeck process. In addition to consumption and purchasing life insurance, the wage earner invests his wealth in the financial market, which consists of a risk-free asset, a market index, and a pair of risky assets with mispricing. Our aim is to maximize the expected utilities obtained from consumption, bequest, or his wealth at the end of the decision horizon. With the dynamic programming approach, we obtain explicit solutions for the optimization problem by solving the corresponding HJB equation. Finally, several numerical examples are presented to illustrate our results.

关键词： Mispricing Model ambiguity Optimal investment strategy Life insurance dynamic programming approach

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Optimal consumption and portfolio selection with lower and upper bounds on consumption

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ADVANCES IN DIFFERENCE EQUATIONS 2020年第1期2020卷 1-11页

作者： Roh, Kum-Hwan Shin, Yong Hyun Hannam Univ Dept Math Daejeon 34430 South Korea Sookmyung Womens Univ Dept Math Seoul 04310 South Korea Sookmyung Womens Univ Res Inst Nat Sci Seoul 04310 South Korea

We investigate the optimal consumption and investment problem with lower and upper bounds on consumption constraints. We derive closed-form solutions by means of the dynamic programming approach. We also evaluate the effects of the optimal consumption and portfolio on consumption constraints and present some numerical/economic implications. In particular, we see that the upper bound on consumption acts as a bliss level in a quadratic utility model.

关键词： Consumption constraints Consumption Investment problem CRRA utility dynamic programming approach

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Optimal Reinsurance and Investment Strategy for an Insurer in a Model with Delay and Jumps

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2020年第2期22卷 777-801页

作者： Zhang, Qiang Chen, Ping Ningxia Univ Sch Math & Stat Yinchuan 750021 Ningxia Peoples R China Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Peoples R China

This paper studies an optimal excess-of-loss reinsurance and investment problem in a model with delay and jumps for an insurer, who can purchase excess-of-loss reinsurance and invest his surplus in a risk-free asset and a risky asset whose price is governed by a jump-diffusion model. The insurer's surplus is described by a diffusion model, which is an approximation of the classical compound Poisson risk model. In particular, the wealth process of the insurer is modeled by a stochastic differential delay equation via introducing the performance-related capital inflow or outflow. Under the criterion for maximizing the expected exponential utility of the combination of terminal wealth and average performance wealth, optimal strategy and the corresponding value function are obtained by using the dynamic programming approach. Finally, numerical examples are provided to show the effects of model parameters on the optimal strategies and illustrate the economic meaning.

关键词： Excess-of-loss reinsurance Jump-diffusion model Stochastic differential delay equation Exponential utility dynamic programming approach

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The optimal multi-period hedging model of currency futures and options with exponential utility

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2020年 366卷 112412-000页

作者： Yu, Xing Wan, Zhongkai Tu, Xiaowen Li, Yanyin Cent China Normal Univ Sch Econ & Business Adm Wuhan 430079 Hubei Peoples R China

In this paper, we consider the optimal cross-hedging and risk control problem of a competitive firm facing exchange risk exposure in a multi-period setting. We present the optimal positions of currency futures and options to maximize the exponential utility of the terminal wealth by dynamic programming approach. To evaluate the potential effectiveness of cross-hedging with currency futures and options, we compare terminal wealth, utility based on terminal wealth and variance of the wealth accumulation path in three cases: hedging with futures and options, net futures hedging and no hedging. An empirical study of two cross-exchange rates of USD/EUR and CNY/USD is performed. The results show that cross-exchange rate futures and options always offer the firm an improved ability to hedge against the foreign exchange rate risks. Relative to no hedging, cross-hedging with currency futures and options or net currency futures hedging achieves positive returns. As the risk aversion coefficient increases, the firm's profit of futures hedging increases, while the profit of options hedging decreases. We suggest the firm with smaller risk aversion coefficient choose options hedging, and the firm with higher risk aversion coefficient choose futures hedging. Furthermore, when using currency derivatives for hedging, the wealth volatility also decreases significantly. Thus, for the multinational firms, cross-currency hedging is an efficient risk management technique to reduce their foreign exchange risk exposure. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Risk management dynamic cross-hedging Currency futures Currency option dynamic programming approach

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Optimization of Decision Rules Relative to Length - Comparative Study 39th

Optimization of Decision Rules Relative to Length - Comparat...

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39th International Conference on Information Systems Architecture and Technology (ISAT)

作者： Zielosko, Beata Zabinski, Krzysztof Univ Silesia Katowice Inst Comp Sci 39 Bedzinska St PL-41200 Sosnowiec Poland

ISBN: (纸本)9783319999968;9783319999951

The paper presents a modification of a dynamic programming approach employed for decision rules optimization with respect to their length. There are two aspects taken into account: (i) consideration on the length of approximate decision rules and (ii) consideration on the size of a directed acyclic graph constructed by the modified algorithm.

关键词： Decision rules Length Optimization dynamic programming approach

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Optimization of Approximate Decision Rules Relative to Length 14th

Optimization of Approximate Decision Rules Relative to Lengt...

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14th International Scientific Conference on Beyond Databases, Architectures, and Structures (BDAS) Held at the 24th IFIP World Computer Congress (IFIP WCC)

作者： Zielosko, Beata Zabinski, Krzysztof Univ Silesia Katowice Inst Comp Sci 39 Bedzinska St PL-41200 Sosnowiec Poland

In the paper, a modified dynamic programming approach for optimization of decision rules relative to length is studied. Experimental results connected with length of approximate decision rules, size of a directed acyc... 详细信息

ISBN: (纸本)9783319999876

关键词： Decision rules dynamic programming approach Optimization Length

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Energy efficient scheduling problems under Time-Of-Use tariffs with different energy consumption of the jobs

Energy efficient scheduling problems under Time-Of-Use tarif...

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16th IFAC Symposium on Information Control Problems in Manufacturing (INCOM)

作者： Aghelinejad, MohammadMohsen Ouazene, Yassine Yalaoui, Alice Univ Technol Troyes CNRS Ind Syst Optimizat Lab ICDUMR 6281 Troyes France

This paper deals with single machine scheduling problems, where the machine may be in processing, idle or off state. The machine consumes a different amount of energy in function of its state. Moreover, during processing (ON state), the energy consumption depends on the job. The complexity of these problems, when the jobs' sequence is fix, for the uniform-speed problem and the speed-scalable problem are analyzed. For this purpose, a dynamic programming approach is proposed to solve these problems by using a finite graph. The results demonstrate that the uniform-speed problem is polynomial of degree 3, and its speed-scalable case is pseudo polynomial. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Energy efficiency Time of use electricity tariffs Non-preemption Single machine scheduling dynamic programming approach Speed scalable problem

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