A Maximum Principle via Malliavin calculus for combined stochastic control and impulse control of forward‐backward systems

Wang, Yan; Song, Aimin; Feng, Enmin

doi:10.1002/asjc.1097

Cited by 7 publications

(4 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where a(ω) ≥ 0 is G t −measurable and bounded, and δ t (s) is the unit point mass at t. In this case, we obtain by (23) that…”

Section: R0rmentioning

confidence: 87%

See 1 more Smart Citation

Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer

Wang¹,

Zhao²,

Wang³

et al. 2018

Journal of Industrial &Amp; Management Optimization

Self Cite

View full text Add to dashboard Cite

We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer.

show abstract

“…where a(ω) ≥ 0 is G t −measurable and bounded, and δ t (s) is the unit point mass at t. In this case, we obtain by (23) that…”

Section: R0rmentioning

confidence: 87%

“…That is, the insurer decides the investment strategy and dividend payment policy based on partial information, which is less than the full information generated by the market events (see, e.g. [4,19,23]). From the view of control theory, such a problem can be generalized as a novel regular-singular stochastic control problem with partial information.…”

mentioning

confidence: 99%

Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer

Wang¹,

Zhao²,

Wang³

et al. 2018

Journal of Industrial &Amp; Management Optimization

Self Cite

View full text Add to dashboard Cite

show abstract

“…Different impulsive control strategies can make unstable systems uniformly stable, asymptotically stable, or exponentially stable [13,35,36]. Studies have examined the asymptotic stability of impul-sive control systems with fixed impulse times [37]. Li et al further studied the exponential stabilization of time-delay systems, concluding that impulsive control with delayed impulses can exponentially stabilize unstable systems [38].…”

Section: Introductionmentioning

confidence: 99%

Exponential stability of time‐delay systems with flexible delayed impulse

Ling

Liu

2023

Asian Journal of Control

View full text Add to dashboard Cite

The problem of exponential stability for time‐delay systems with flexible delayed impulse control is investigated. Unlike the conventional Razumikhin‐type inequality, variable parameter based on the flexible impulsive gain is introduced. Sufficient conditions for exponential stability are developed for a class of time‐delay systems, for which the size of delay is not limited by impulsive intervals. A flexible impulse control scheme is developed by utilizing the flexible impulsive gain and time‐varying delays. When the system is disturbed by the impulse interferences, both the impulse gain and impulse delay can be adjusted accordingly to make the system exponential stable. The effectiveness of the present results is illustrated by two numerical examples and an application.

show abstract

“…Impulse control is an artificial control strategy that is cheaper and simpler to operate compared with other control strategies. At present, the impulse control technique has been put into use in many fields . In view of this, impulse control is applied to achieve a stable state in this paper.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Stability Criterion for the Nonlinear Fractional‐Order Three‐Dimensional Financial System with Delay

Zhang

Cheng

et al. 2018

Asian Journal of Control

View full text Add to dashboard Cite

In this paper, we study the dynamic characteristics of fractional-order nonlinear financial systems, including bifurcation and local asymptotic stability. Among them, we select the elasticity of demand of commercial (EDC) as the bifurcation point to discuss the state of the system. By calculating, the lowest order bifurcation point is obtained. Furthermore, the impulse control gains that follow a fractional-order control law are applied to make the fractional-order nonlinear financial system stable. In addition, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed state form of the system near the bifurcation point and the states of the system when the impulse control is used or not.

show abstract

A Maximum Principle via Malliavin calculus for combined stochastic control and impulse control of forward‐backward systems

Cited by 7 publications

References 35 publications

Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer

Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer

Exponential stability of time‐delay systems with flexible delayed impulse

Bifurcation Analysis and Stability Criterion for the Nonlinear Fractional‐Order Three‐Dimensional Financial System with Delay

Contact Info

Product

Resources

About