Ruin probabilities in the presence of regularly varying tails and optimal investment

Gaier, Johanna; Grandits, Peter

doi:10.1016/s0167-6687(02)00101-4

Cited by 34 publications

(22 citation statements)

References 9 publications

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“…This stresses once more the importance of a proper asset-liability management of an insurance company. A complementary result about the asymptotic ruin probabilities for large claims can be found in Gaier and Grandits [6].…”

Section: Introductionmentioning

confidence: 61%

Asymptotic ruin probabilities and optimal investment

Gaier¹,

Grandits²,

Schachermayer³

2003

Ann. Appl. Probab.

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Abstract. We study the infinite time ruin probability for an insurance company in the classical Cramér-Lundberg model with finite exponential moments. The additional non-classical feature is that the company is also allowed to invest in some stock market, modeled by geometric Brownian motion. We obtain an exact analogue of the classical estimate for the ruin probability without investment, i.e. an exponential inequality. The exponent is larger than the one obtained without investment, the classical Lundberg adjustment coefficient, and thus one gets a sharper bound on the ruin probability. A surprising result is that the trading strategy yielding the optimal asymptotic decay of the ruin probability simply consists in holding a fixed quantity (which can be explicitly calculated) in the risky asset, independent of the current reserve. This result is in apparent contradiction to the common believe that 'rich' companies should invest more in risky assets than 'poor' ones. The reason for this seemingly paradoxical result is that the minimization of the ruin probability is an extremely conservative optimization criterion, especially for 'rich' companies.

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Section: Introductionmentioning

confidence: 61%

Asymptotic ruin probabilities and optimal investment

Gaier¹,

Grandits²,

Schachermayer³

2003

Ann. Appl. Probab.

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“…In this short note we aim to extend the result of Gaier and Grandits [2] in parallel to the case of extended regular variation.…”

Section: Introductionmentioning

confidence: 93%

“…When the insurance company is allowed to invest a portion of its surplus into a stock whose price is described by a geometric Brownian motion, an optimal investment strategy in the sense of minimizing the ruin probability was proposed by Hipp and Plum [3] . For the case that the distribution of claim sizes is regularly-varying tailed with index for some < −1, following Hipp and Plum's [3] idea of optimal investment, Gaier and Grandits [2] proved that the corresponding ruin probability considered as a function of the initial surplus is also regularly varying with the same index.…”

Section: Introductionmentioning

confidence: 99%

The ruin probability in the presence of extended regular variation and optimal investment

Wei

2008

Acta Math. Appl. Sin. Engl. Ser.

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Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.

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“…considered in Hipp and Schmidli [65], Gaier and Grandits [46] and Gaier et al [47]. Another possibility to reduce the probability of ruin in the classical model is to use reinsurance.…”

Section: Reinsurance and Investmentmentioning

confidence: 99%