Legendre Transform-Dual Solution for a Class of Investment and Consumption Problems with HARA Utility

Chang, Hao; Rong, Ximin

doi:10.1155/2014/656438

Cited by 10 publications

(5 citation statements)

References 14 publications

(25 reference statements)

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“…In the existing literature, 𝐺(𝜆, 𝑡) rather than V(𝜆, 𝑡) seems to be preferably taken to solve for the dual PDE and hence the original primal one; also see (Chang & Chang, 2017;Chang & Rong, 2014;Gao, 2008Gao, , 2009Gao, , 2010Jonsson & Sircar, 2002;Jung & Kim, 2012;Xiao et al, 2007), to name a few.…”

Section: Appendix E: On Applicability Of Common Arguments For the Cla...mentioning

confidence: 99%

Inter‐temporal mutual‐fund management

Bensoussan

Cheung

et al. 2022

Mathematical Finance

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Traditionally, mutual funds are mostly managed via an ad hoc approach, namely a terminal‐only optimization. Due to the intricate mathematical complexity of a continuum of constraints imposed, effects of the inter‐temporal reward for the managers are essentially neglected in the previous literature. For instance, the inter‐temporal optimal investment problem from the fund manager's viewpoint, who earns proportional management fees continuously (a golden rule in practice), has been outstanding for long. This article completely resolves this challenging question especially under generic running and terminal utilities, via the Dynamic Programming Principle which leads to a nonconventional, highly nonlinear HJB equation. We develop an original mathematical analysis to establish the unique existence of the classical solution of the primal problem. Further numerical calibrations and simulations for both the portfolio weight and the value functions illustrate the robustness of the optimal portfolio towards the manager's risk attitude, which allows different managers with various risk characteristics to sell essentially the same investment vehicle. Simulation studies also indicate that the policy of charging a substantial terminal‐only management fee can be replaced by another one with only a negligible amount over the interim period, which substantially reduces the total management fee paid by the clients without lowering the manager's satisfaction at all; this last observation echoes the magic of the alchemy of finance.

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Section: Appendix E: On Applicability Of Common Arguments For the Cla...mentioning

confidence: 99%

Inter‐temporal mutual‐fund management

Bensoussan

Cheung

et al. 2022

Mathematical Finance

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“…During the course of online sales, even a small outage can lead to a lot of damage. Cloud load balancing is all about distributing the workloads over a wide array of computing resources [48]. This limits the costs connected with report administration systems.…”

Section: Applications Of Load Balancingmentioning

confidence: 99%

A Systematic Analysis of Load Balancing in Cloud Computing

Bezawada

Marella

Gunasekhar

2019

International Journal of Simulation: Systems, Science &Amp; Technology

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Cloud Computing is an ever growing area in information technology. It is internet based technology which emphasizes its utility and follows pay-as-you-go model. It is at present turning into the favoured strategy for communication and computation over scalable networks because of various attractive qualities such as high accessibility, adaptability, scalability, simplicity of management, fault tolerance and minimal effort of possession. The data processing and storage volume is increasing rapidly in cloud environment, which prompts an uneven dissemination of overall work on cloud resources. So a legitimate balance of overall load balancing over the available resources is a major issue in cloud computing paradigm. It is a technique which uses multiple nodes and distributes dynamic workload among them so that no single node is overloaded. It enhances system performance and legitimate utilization of resources. It also limits the time and cost engaged with such huge computing models. Load balancing and better resource utilization is provided by many existing algorithms. This paper explores the various load balancing algorithms related to the cloud.

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“…According to (18), we say that is a stochastic process capturing the value of private information and then obtain the solution…”

Section: Proposition the Agent's Continuation Value Can Be Uniquelymentioning

confidence: 99%

“…Reference [17] uses Legendre transform-dual theory to solve the optimal investment problem based on hyperbolic absolute risk aversion (HARA) preference under constant elastic variance model. References [18,19] study the investment-consumption of HARA utility by Legendre method.…”

Section: Introductionmentioning

confidence: 99%

A Solvable Time-Inconsistent Principal-Agent Problem

Qiu

2018

Discrete Dynamics in Nature and Society

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We consider the dynamic contract model with time inconsistency preference of principal-agent problem to study the influence of the time inconsistency preference on the optimal effort and the optimal reward mechanism. We show that when both the principal and the agent are time-consistent, the optimal effort and the optimal reward are the decreasing functions of the uncertain factor. And when the agent is time-inconsistent, the impatience of the agent has a negative impact on the optimal contract. The higher the discount rate of the agent is, the lower the efforts provided; agents tend to the timely enjoyment. In addition, when both the principal and the agent are time-inconsistent, in a special case, their impatience can offset the impact of uncertainty factor on the optimal contract, but, in turn, their impatience will affect the contract.

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Legendre Transform-Dual Solution for a Class of Investment and Consumption Problems with HARA Utility

Cited by 10 publications

References 14 publications

Inter‐temporal mutual‐fund management

Inter‐temporal mutual‐fund management

A Systematic Analysis of Load Balancing in Cloud Computing

A Solvable Time-Inconsistent Principal-Agent Problem

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