On One-Dimensional Stochastic Differential Equations Involving the Maximum Process

Belfadli, Rachid; Hamadène, Saïd; Ouknine, Youssef

doi:10.1142/s0219493709002671

Cited by 15 publications

(3 citation statements)

References 15 publications

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“…t . Under Assumption 2, the existence and uniqueness of the solution to Equation (2.8) can be obtained by a method very close to the one in Belfadli et al [9]. On the other hand, we can also present a implicit expression to the solution of Equation (2.8) as the one in [33].…”

mentioning

confidence: 73%

Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax

Xu¹,

Yao²,

Cheng³

2020

Journal of Industrial &Amp; Management Optimization

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This study examines the optimal investment and dividend problem for an insurer with CRRA preference. The insurer's goal is to maximize the expected discounted accumulated utility from dividend before ruin and the insurer subjects to high gain tax payment. Both the surplus process and the financial market are modulated by an external Markov chain. Using the weak dynamic programming principle (WDPP), we prove that the value function of our control problem is the unique viscosity solution to coupled Hamilton-Jacobi-Bellman (HJB) equations with first derivative constraints. Solving an auxiliary problem without regime switching, we prove that, it is optimal for the insurer in a multiple-regime market to adopt the policies in the same way as in a single-regime market. The regularity of the viscosity solution on its domain is proved and thus the HJB equations admits classical solution. A numerical scheme for the value function is provided by the Markov chain approximation method, two numerical examples are given to illustrate the impact of the high gain tax and regime switching on the optimal policies.

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confidence: 73%

Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax

Xu¹,

Yao²,

Cheng³

2020

Journal of Industrial &Amp; Management Optimization

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“…Remark 5.2. While this paper was in review, we became aware of [2], which contains an existence result for (5.1) covering α = β = −1.…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

“…To do this, we need to rewrite vr in a more suitable form. Introduce the notation X (1) (t) = (X 1 (t), X 2 (0), X 3 (0)), X (2) (t) = (X 1 (0), X 2 (2), X 3 (0)) and X (3) (t) = (X 1 (0), X 2 (0), X 3 (t)) for each t ≥ 0. We define ρ (i) to be the absorption time of X i , that is,…”

Section: )mentioning

confidence: 99%

Minimizing the time to a decision

Jacka¹,

Warren²,

Windridge³

2011

Ann. Appl. Probab.

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Suppose we have three independent copies of a regular diffusion on $[0,1]$ with absorbing boundaries. Of these diffusions, either at least two are absorbed at the upper boundary or at least two at the lower boundary. In this way, they determine a majority decision between 0 and 1. We show that the strategy that always runs the diffusion whose value is currently between the other two reveals the majority decision whilst minimizing the total time spent running the processes.Comment: Published in at http://dx.doi.org/10.1214/10-AAP737 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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On the Pathwise Uniqueness of Solutions of One-dimensional Reflected Stochastic Differential Equations with Jumps

Zhang

2024

Acta Math. Appl. Sin. Engl. Ser.

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On One-Dimensional Stochastic Differential Equations Involving the Maximum Process

Cited by 15 publications

References 15 publications

Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax

Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax

Minimizing the time to a decision

On the Pathwise Uniqueness of Solutions of One-dimensional Reflected Stochastic Differential Equations with Jumps

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