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The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literature for a dual risk…

Risk Management · Quantitative Finance 2022-12-08 Arash Fahim , Lingjiong Zhu

This paper considers an insurer with two collaborating business lines, and the risk exposure of each line follows a diffusion risk model. The manager of the insurer makes three decisions for each line: (i) dividend payout, (ii)…

Optimization and Control · Mathematics 2025-08-12 Tim J. Boonen , Engel John C. Dela Vega , Bin Zou

This paper studies the bail-out optimal dividend problem with regime switching under the constraint that the cumulative dividend strategy is absolutely continuous. We confirm the optimality of the regime-modulated refraction-reflection…

Mathematical Finance · Quantitative Finance 2020-02-10 Kei Noba , José-Luis Pérez , Xiang Yu

We study the optimal dividend problem in the dual model where dividend payments can only be made at the jump times of an independent Poisson process. In this context, Avanzi et al. [5] solved the case with i.i.d. hyperexponential jumps;…

Probability · Mathematics 2017-08-15 José-Luis Pérez , Kazutoshi Yamazaki

Banks must optimize risky investments, dividend payouts, and capital structure under tight Basel III solvency and liquidity constraints, while costly equity issuance serves as a distress-recovery tool. We formulate this as a stochastic…

Optimization and Control · Mathematics 2026-03-17 Erhan Bayraktar , Etienne Chevalier , Vathana Ly Vath , Yuqiong Wang

We consider the multi-refraction strategies in two equivalent versions of the optimal dividend problem in the dual (spectrally positive L\'evy) model. The first problem is a variant of the bail-out case where both dividend payments and…

Probability · Mathematics 2018-03-19 Irmina Czarna , José Luis Pérez , Kazutoshi Yamazaki

In this paper, we study an optimal dividend and capital-injection problem in a Cram\'er--Lundberg model where claim arrivals follow a Hawkes process, capturing clustering effects often observed in insurance portfolios. We establish key…

Optimization and Control · Mathematics 2025-11-27 Paulin Aubert , Etienne Chevalier , Vathana Ly Vath

In this paper we consider a modified version of the classical optimal dividends problem of de Finetti in which the dividend payments subject to a penalty at ruin. We assume that the risk process is modeled by a general spectrally positive…

Pricing of Securities · Quantitative Finance 2013-02-26 Chuancun Yin , Yuzhen Wen

This study considers an optimal reinsurance, investment, and dividend strategy control problem for insurance companies in a regulated Markov regime-switching environment, intending to maximize long-run average reward. Unlike existing single…

Optimization and Control · Mathematics 2025-12-18 Lingjia Zeng , Manman Li

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical dividend problem for an insurance…

Probability · Mathematics 2008-12-10 Florin Avram , Zbigniew Palmowski , Martijn R. Pistorius

We consider a diffusion risk model where dividends are paid at rate $U(t) \in [0, u_0]$. We are interested in maximising the dividend payments under a drawdown constraint, that is, we penalise a drawdown size larger than a level $d > 0$. We…

Optimization and Control · Mathematics 2025-11-06 Kira Dudziak , Hanspeter Schmidli

Motivated by recent developments in risk management based on the U.S. bankruptcy code, we revisit the De Finetti's optimal dividend problem by incorporating the reorganization process and regulator's intervention documented in Chapter 11…

Optimization and Control · Mathematics 2023-11-07 Wenyuan Wang , Xiang Yu , Xiaowen Zhou

This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments). The management of the company is assumed to…

Probability · Mathematics 2015-06-22 F. Avram , Z. Palmowski , M. R. Pistorius

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose…

Pricing of Securities · Quantitative Finance 2014-02-26 Ying Shen , Chuancun Yin , Kam Chuen Yuen

In this paper, we model the cash surplus (or equity) of a risky business with a Brownian motion. Owners can take cash out of the surplus in the form of "dividends", subject to transaction costs. However, if the surplus hits 0 then ruin…

Risk Management · Quantitative Finance 2021-08-19 Benjamin Avanzi , Hayden Lau , Bernard Wong

Avanzi et al. (2016) recently studied an optimal dividend problem where dividends are paid both periodically and continuously with different transaction costs. In the Brownian model with Poissonian periodic dividend payment opportunities,…

Optimization and Control · Mathematics 2018-01-16 José-Luis Pérez , Kazutoshi Yamazaki

In this paper, we focus on the problem of optimal portfolio-consumption policies in a multi-asset financial market, where the n risky assets follow Exponential Ornstein-Uhlenbeck processes, along with one risk-free bond. The investor's…

Optimization and Control · Mathematics 2025-09-10 Zhaoxiang Zhong , Haiming Song

We re-visit the classical problem of optimal payment of dividends and determine the degree to which the diffusion approximation serves as a valid approximation of the classical risk model for this problem. Our results parallel some of those…

Optimization and Control · Mathematics 2020-10-26 Asaf Cohen , Virginia R. Young

We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…

Optimization and Control · Mathematics 2025-03-24 Dariusz Zawisza

This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that…

Mathematical Finance · Quantitative Finance 2024-06-25 J. Cerda-Hernandez , A. Sikov , A. Ramos