Dividend barrier strategy: Proceed with caution

2018 ◽  
Vol 137 ◽  
pp. 157-164 ◽  
Author(s):  
Kristina P. Sendova ◽  
Chen Yang ◽  
Ruixi Zhang
Keyword(s):  
Barrier Strategy

scholarly journals On optimality of the barrier strategy for a general Lévy risk process

2011 ◽  
Vol 53 (9-10) ◽  
pp. 1700-1707 ◽  
Author(s):  
Kam Chuen Yuen ◽  
Chuancun Yin
Keyword(s):  
Risk Process ◽  
Barrier Strategy

scholarly journals On the improved thinning risk model under a periodic dividend barrier strategy

2021 ◽  
Vol 6 (12) ◽  
pp. 13448-13458
Author(s):  
Fuyun Sun ◽  
◽  
Yuelei Li ◽  
Keyword(s):  
Integral Equations ◽  
Counting Process ◽  
Risk Model ◽  
Insurance Companies ◽  
Barrier Strategy ◽  
Improved Model ◽  
The Impact ◽  
Thinning Process ◽  
Explicit Expressions

<abstract><p>In this study, we consider a periodic dividend barrier strategy in an improved thinning risk model, which indicates that insurance companies randomly receive premiums and pay dividends. In the improved model, the premium is stochastic, and the claim counting process is a p-thinning process of the premium counting process. The integral equations satisfied by the Gerber-Shiu function and the expected discounted cumulative dividend function are derived. Explicit expressions of those actuarial functions are obtained when the claim and premium sizes are exponentially distributed. We analyze and illustrate the impact of various parameters on them and obtain the optimal barrier. Finally, a conclusion is drawn.</p></abstract>

scholarly journals On a Dual Model with Barrier Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yuzhen Wen ◽  
Chuancun Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Generating Function ◽  
Risk Model ◽  
Moment Generating Function ◽  
Dual Model ◽  
Barrier Strategy ◽  
Dividend Payments ◽  
The Moment

We consider the dual of the generalized Erlang(n)risk model with a barrier dividend strategy. We derive integro-differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment-generating function of the discounted dividend payments until ruin, respectively. The results are illustrated by several examples.

scholarly journals The moments of the discounted loss and the discounted dividends for a spectrally negative Lévy risk process

2015 ◽  
Vol 52 (03) ◽  
pp. 665-687
Author(s):  
Esther Frostig
Keyword(s):  
Lévy Process ◽  
Infinite Horizon ◽  
Risk Process ◽  
Levy Process ◽  
Dual Model ◽  
Exit Times ◽  
Barrier Strategy ◽  
Spectrally Negative Lévy Process

Consider a spectrally negative risk process where, on ruin, the deficit is immediately paid, and the process restarts from 0. When the process reaches a threshold b, all the surplus above b is paid as dividend. Applying the theory of exit times for a spectrally negative Lévy process and its reflection at the maximum and at the minimum, we obtain recursive formulae for the following moments. (i) The moments of the discounted loss until the process reaches b. This is equivalent to the moments of the discounted dividends in the dual model under the barrier strategy. (ii) The moments of the discounted loss for models with and without a dividend barrier for the infinite horizon. (iii) The moments of the discounted dividends for the infinite horizon.

scholarly journals Dividend Problems in the Diffusion Model with Interest and Exponentially Distributed Observation Time

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Cuilian Wang ◽  
Xiao Liu
Keyword(s):  
Laplace Transform ◽  
Diffusion Model ◽  
Generating Function ◽  
Moment Generating Function ◽  
Observation Time ◽  
Integrodifferential Equations ◽  
Barrier Strategy ◽  
Ruin Time ◽  
The Laplace Transform ◽  
The Moment

Consider dividend problems in the diffusion model with interest and exponentially distributed observation time where dividends are paid according to a barrier strategy. Assume that dividends can only be paid with a certain probability at each point of time; that is, on each observation, if the surplus exceeds the barrier level, the excess is paid as dividend. In this paper, integrodifferential equations for the moment-generating function, thenth moment function, and the Laplace transform of ruin time are derived; explicit expressions for the expected discounted dividends paid until ruin and the Laplace transform of ruin time are also obtained.

scholarly journals The Løkka–Zervos Alternative for a Cramér–Lundberg Process with Exponential Jumps

Risks ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 120
Author(s):  
Florin Avram ◽  
Dan Goreac ◽  
Jean-François Renaud
Keyword(s):  
Brownian Motion ◽  
Cost Of Capital ◽  
Diffusion Processes ◽  
Risk Process ◽  
Insurance Company ◽  
Barrier Strategy ◽  
First Passage ◽  
Double Barrier ◽  
The Cost ◽  
Capital Injections

In this paper, we study a stochastic control problem faced by an insurance company allowed to pay out dividends and make capital injections. As in (Løkka and Zervos (2008); Lindensjö and Lindskog (2019)), for a Brownian motion risk process, and in Zhu and Yang (2016), for diffusion processes, we will show that the so-called Løkka–Zervos alternative also holds true in the case of a Cramér–Lundberg risk process with exponential claims. More specifically, we show that: if the cost of capital injections is low, then according to a double-barrier strategy, it is optimal to pay dividends and inject capital, meaning ruin never occurs; and if the cost of capital injections is high, then according to a single-barrier strategy, it is optimal to pay dividends and never inject capital, meaning ruin occurs at the first passage below zero.

Morphological diagram of a nucleating agent/poly(ε-caprolactone) and an in situ barrier strategy

RSC Advances ◽  
2015 ◽  
Vol 5 (97) ◽  
pp. 79687-79690 ◽  
Author(s):  
Siqi Wu ◽  
Rui Han ◽  
Min Nie ◽  
Qi Wang
Keyword(s):  
Nucleating Agent ◽  
Nucleating Agents ◽  
Barrier Strategy

A temperature/composition morphological diagram of nucleating agent/poly(ε-caprolactone) blends to direct in situ formation of flake nucleating agents was constructed.

scholarly journals The moments of the discounted loss and the discounted dividends for a spectrally negative Lévy risk process

2015 ◽  
Vol 52 (3) ◽  
pp. 665-687
Author(s):  
Esther Frostig
Keyword(s):  
Lévy Process ◽  
Infinite Horizon ◽  
Risk Process ◽  
Levy Process ◽  
Dual Model ◽  
Exit Times ◽  
Barrier Strategy ◽  
Spectrally Negative Lévy Process

Consider a spectrally negative risk process where, on ruin, the deficit is immediately paid, and the process restarts from 0. When the process reaches a threshold b, all the surplus above b is paid as dividend. Applying the theory of exit times for a spectrally negative Lévy process and its reflection at the maximum and at the minimum, we obtain recursive formulae for the following moments. (i) The moments of the discounted loss until the process reaches b. This is equivalent to the moments of the discounted dividends in the dual model under the barrier strategy. (ii) The moments of the discounted loss for models with and without a dividend barrier for the infinite horizon. (iii) The moments of the discounted dividends for the infinite horizon.

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