Ruin theory with stochastic return on investments

Paulsen, Jostein; Gjessing, Håkon K.

doi:10.1017/s0001867800047972

Cited by 73 publications

(116 citation statements)

References 6 publications

Supporting

Mentioning

114

Contrasting

Unclassified

Order By: Relevance

“…The integral term represents the additional income resulting from the constant force of interest i > 0 on the free surplus (see for instance Paulsen [9], where the existence of such a process R is proved). A similar model was dealt with in Albrecher et al [2] and Paulsen & Gjessing [10,11]. In this paper we are interested in identifying the optimal strategy to pay out dividends from process (1) to shareholders during the period of solvency.…”

Section: Introductionmentioning

confidence: 97%

Optimal dividend strategies for a risk process under force of interest

Albrecher

Thonhauser

2008

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

In the classical Cramér-Lundberg model in risk theory the problem of maximizing the expected cumulated discounted dividend payments until ruin is a widely discussed topic. In the most general case within that framework it is proved (Gerber (1969), Azcue & Muler (2005), Schmidli (2007)) that the optimal dividend strategy is of band type. In the present paper we discuss this maximization problem in a generalized setting including a constant force of interest in the risk model. The value function is identied in the set of viscosity solutions of the associated Hamilton-Jacobi-Bellman equation and the optimal dividend strategy in this risk model with interest is derived, which in the general case is again of band type and for exponential claim sizes collapses to a barrier strategy. Finally, an example is constructed for Erlang(2)-claim sizes, in which the bands for the optimal strategy are explicitly calculated.

show abstract

Section: Introductionmentioning

confidence: 97%

Optimal dividend strategies for a risk process under force of interest

Albrecher

Thonhauser

2008

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

show abstract

“…In this case, under weak assumptions, ψ is twice continuously differentiable on (0, ∞) and is a solution of the equation, see [25,49,69] and in particular [26],…”

Section: Some General Results In the Markov Modelmentioning

confidence: 99%

“…Extensions beyond that seem very difficult though. In [49] the case with σ P > 0 and claims exponentially distributed was also solved, and this solution was extended in [10] with separate solutions for ψ d (y) and ψ s (y).…”

Section: Analytical and Numerical Solutionsmentioning

confidence: 99%

Ruin Models with Investment Income

Paulsen

2010

Encyclopedia of Quantitative Finance

Self Cite

View full text Add to dashboard Cite

This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integrodifferential equations, exact and numerical solutions, asymptotic results, bounds on the ruin probability and also the possibility of minimizing the ruin probability by investment and possibly reinsurance control. The main emphasis is on continuous time models, but discrete time models are also covered. A fairly extensive list of references is provided, particularly of papers published after 1998. For more references to papers published before that, the reader can consult [47].

show abstract

“…Then ) ( y ψ is the probability of ultimate ruin when initial capital is y and it is well known [14] that satisfies the integrodifferential equation…”

Section: The Model and Theoretical Resultsmentioning

confidence: 99%

Numerical Ultimate Ruin Probabilities under Interest Force

Kasozi¹,

Paulsen²

2005

J. of Mathematics and Statistics

Self Cite

View full text Add to dashboard Cite

This work addresses the issue of ruin of an insurer whose portfolio is exposed to insurance risk arising from the classical surplus process. Availability of a positive interest rate in the financial world forces the insurer to invest into a risk free asset. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block method in conjuction with the Simpson rule to solve the Volterra equation for ultimate ruin. This probability is arrived at by taking a linear combination of some two solutions to the Volterra integral equation. The several numerical examples given show that our results are excellent and reliable.

show abstract

Ruin theory with stochastic return on investments

Cited by 73 publications

References 6 publications

Optimal dividend strategies for a risk process under force of interest

Optimal dividend strategies for a risk process under force of interest

Ruin Models with Investment Income

Numerical Ultimate Ruin Probabilities under Interest Force

Contact Info

Product

Resources

About