Optimal dividend-financing strategies in a dual risk model with time-inconsistent preferences

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual risk model, under a stochastic interest rate, assuming the discounting factor follows a geometric Brownian motion or exponential Lévy process. We will show that closed form solutions can be obtained.

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The dual risk model under a mixed ratcheting and periodic dividend strategy

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2021.1974483 ◽

2021 ◽

pp. 1-15

Author(s):

Zhan-Jie Song ◽

Fu-Yun Sun

Keyword(s):

Risk Model ◽

Dual Risk Model

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SOME ADVANCES ON THE ERLANG(n) DUAL RISK MODEL

Astin Bulletin ◽

10.1017/asb.2014.19 ◽

2014 ◽

Vol 45 (1) ◽

pp. 127-150 ◽

Cited By ~ 10

Author(s):

Eugenio V. Rodríguez-Martínez ◽

Rui M. R. Cardoso ◽

Alfredo D. Egídio dos Reis

Keyword(s):

Risk Model ◽

Waiting Times ◽

Dual Model ◽

Time Of Ruin ◽

Constant Rate ◽

Dual Risk Model ◽

The Laplace Transform ◽

The Time Of Ruin ◽

Renewal Risk ◽

The Individual

AbstractThe dual risk model assumes that the surplus of a company decreases at a constant rate over time and grows by means of upward jumps, which occur at random times and sizes. It is said to have applications to companies with economical activities involved in research and development. This model is dual to the well-known Cramér-Lundberg risk model with applications to insurance. Most existing results on the study of the dual model assume that the random waiting times between consecutive gains follow an exponential distribution, as in the classical Cramér-Lundberg risk model. We generalize to other compound renewal risk models where such waiting times are Erlang(n) distributed. Using the roots of the fundamental and the generalized Lundberg's equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Furthermore, we compute expected discounted dividends, as well as higher moments, when the individual common gains follow a Phase-Type, PH(m), distribution. We also perform illustrations working some examples for some particular gain distributions and obtain numerical results.

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Constant barrier strategies in a two-state Markov-modulated dual risk model

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-011-0113-7 ◽

2011 ◽

Vol 27 (4) ◽

pp. 679-690 ◽

Cited By ~ 1

Author(s):

Xue-min Ma ◽

Kui Luo ◽

Guang-ming Wang ◽

Yi-jun Hu

Keyword(s):

Risk Model ◽

Dual Risk Model ◽

Markov Modulated

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ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

Astin Bulletin ◽

10.1017/asb.2014.12 ◽

2014 ◽

Vol 44 (3) ◽

pp. 635-651 ◽

Cited By ~ 63

Author(s):

Chuancun Yin ◽

Yuzhen Wen ◽

Yongxia Zhao

Keyword(s):

Lévy Process ◽

Risk Model ◽

Levy Process ◽

Dual Model ◽

Threshold Strategy ◽

Classical Risk Model ◽

Surplus Process ◽

Optimal Dividend ◽

Special Cases ◽

The Classical Risk Model

AbstractIn this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

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Solvency of an Insurance Company in a Dual Risk Model with Investment: Analysis and Numerical Study of Singular Boundary Value Problems

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542519110022 ◽

2019 ◽

Vol 59 (11) ◽

pp. 1904-1927 ◽

Cited By ~ 2

Author(s):

T. A. Belkina ◽

N. B. Konyukhova ◽

B. V. Slavko

Keyword(s):

Boundary Value Problems ◽

Risk Model ◽

Numerical Study ◽

Boundary Value ◽

Investment Analysis ◽

Singular Boundary ◽

Insurance Company ◽

Singular Boundary Value Problems ◽

Dual Risk Model

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Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

Risks ◽

10.3390/risks6040110 ◽

2018 ◽

Vol 6 (4) ◽

pp. 110 ◽

Cited By ~ 1

Author(s):

Sooie-Hoe Loke ◽

Enrique Thomann

Keyword(s):

Differential Equation ◽

Integral Equation ◽

Ruin Probability ◽

Risk Model ◽

Constant Force ◽

Time Of Ruin ◽

Dual Risk Model ◽

The Laplace Transform ◽

Force Of Interest ◽

The Time Of Ruin

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.

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