91 research outputs found
A State-Dependent Dual Risk Model
In a dual risk model, the premiums are considered as the costs and the claims
are regarded as the profits. The surplus can be interpreted as the wealth of a
venture capital, whose profits depend on research and development. In most of
the existing literature of dual risk models, the profits follow the compound
Poisson model and the cost is constant. In this paper, we develop a
state-dependent dual risk model, in which the arrival rate of the profits and
the costs depend on the current state of the wealth process. Ruin probabilities
are obtained in closed-forms. Further properties and results will also be
discussed.Comment: 20 pages, 4 figure
Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps
In this paper, we propose a stochastic process, which is a Cox-Ingersoll-Ross
process with Hawkes jumps. It can be seen as a generalization of the classical
Cox-Ingersoll-Ross process and the classical Hawkes process with exponential
exciting function. Our model is a special case of the affine point processes.
Laplace transforms and limit theorems have been obtained, including law of
large numbers, central limit theorems and large deviations.Comment: 14 page
Asymptotic Analysis for Optimal Dividends in a Dual Risk Model
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
the dual risk model. It is well known that the value function of this optimal
control problem does not yield closed-form solutions except in some special
cases. In this paper, we study the asymptotics of the optimal dividends problem
when the parameters of the model go to either zero or infinity. Our results
provide insights to the optimal strategies and the optimal values when the
parameters are extreme.Comment: 23 page
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