Ruin probabilities and investment under interest force in the presence of regularly varying tails

Gaier, Johanna; Grandits, Peter

doi:10.1080/03461230410020310

Cited by 33 publications

(27 citation statements)

References 14 publications

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“…In Gaier and Grandits (2003) it shown that, under the assumptions that the claims have regularly varying tail distributions, and that the firm invests a constant fraction of its wealth in the stock market, modeled by geometric Brownian motion, the following holds true…”

Section: Introductionmentioning

confidence: 97%

A Karamata-type theorem and ruin probabilities for an insurer investing proportionally in the stock market

Grandits

2004

Insurance: Mathematics and Economics

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Section: Introductionmentioning

confidence: 97%

A Karamata-type theorem and ruin probabilities for an insurer investing proportionally in the stock market

Grandits

2004

Insurance: Mathematics and Economics

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“…Theorem 3.3 states that the risk process with risky investment defined in (3.3) has Markov property. In practice, the aggregate residual assets amount at time t is often given by Y (t) [15,16] ,…”

Section: A(t) {N (T) T ≥ 0} Is a Poisson Process With Intensity A(t)mentioning

confidence: 99%

Markov process functionals in finance and insurance

Geng

2009

Appl. Math. J. Chin. Univ.

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The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained: the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given. §1 Introduction Markov process functionals have been widely used in economy, finance, engineering and statistic analysis [1][2][3][4] , which have attracted a lot of interest among mathematicians [5][6][7][8] . We have met lots of processes expressed in the form of Markov process functionals especially in describing financial processes and risk processes. How to utilize Markov theory to deal with these processes is one of the problems people are mostly concerned about. For instance, consider a risk model while the rate is adjusted by finite Markov process {υ(s, ω), s ∈ T }, the surplus process {R(t), t ∈ T } is given by [9] Therefore, to study the property of Markov process functionals is of great significance in theory and practice., t ∈ T } has Markov property, if for every bounded measurable function f , 0 < s < t, such that E(f (Y (t))|F Y s ) = E(f (Y (t))|Y (s)).

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“…The first passage problem for this class of processes has been treated extensively, for instance, by Segerdahl (1942), Delbaen and Haezendonck (1987), Garrido (1989), Asmussen and Bladt (1996), Paulsen (1993), Embrechts and Schmidli (1994), Peters (1994), Sundt and Teugels (1995), Gjessing (1997a, 1997b), Dickson and Waters (1999), Norberg (1999), Wang and Wu (2001), Cai and Dickson (2002), Kalashnikov & Norberg (2002), Göing-Jeaschke & Yor (2003), Novikov (2003), Ma and Sun (2003), Wang (2004, 2005), Cai (2004), Cai & Yang (2005), Gaier & Grandits (2004), Paulsen, Kasozi & Steigen (2005) and Gerber & Yang (2007). However, despite of the common previous use of the constant volatility per unit rule, k(U t ) = s r , this assumption may not be regarded as totally realistic in many rational investments.…”

Section: Introductionmentioning

confidence: 99%

The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model

Avram¹,

Usabel²

2008

ASTIN Bull.

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We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004). KEYWORDSFirst passage problems, risk process, stochastic rates of interest, ruin with interest, affine jump-diffusion models, penalty/reward functions at ruin.

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Ruin probabilities and investment under interest force in the presence of regularly varying tails

Cited by 33 publications

References 14 publications

A Karamata-type theorem and ruin probabilities for an insurer investing proportionally in the stock market

A Karamata-type theorem and ruin probabilities for an insurer investing proportionally in the stock market

Markov process functionals in finance and insurance

The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model

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