Classical risk theory in an economic environment

Delbaen, Freddy; Haezendonck, J.

doi:10.1016/0167-6687(87)90019-9

Cited by 96 publications

(36 citation statements)

References 6 publications

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“…Then the aggregate loss process (1) is also referred to be a discounted compound Poisson process. See Delbaen andHaezendonck (1987), Paulsen (1993) and Nilsen and Paulsen (1996) for more details on the distribution of a discounted compound Poisson process.…”

Section: Theorem 1 For Any Continuous Bivariate Functionmentioning

confidence: 99%

Motor Insurance Loss Rate Options and Swaps

Kim

Bae²

2009

SSRN Journal

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Section: Theorem 1 For Any Continuous Bivariate Functionmentioning

confidence: 99%

Motor Insurance Loss Rate Options and Swaps

Kim

Bae²

2009

SSRN Journal

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“…If we drop the assumption that the bond yields zero interest rate, it turns out that the case of zero real interest force i, when the interest force on the bond is equal to the inflation force (cf. Delbaen and Haezendonck [3]), can be treated with essentially the same methods as the ones described above. The stochastic differential equation for the wealth process Y (i) with interest i > 0 is…”

Section: An Asymptotic Inequalitymentioning

confidence: 99%

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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“…The risk processes with interest have been studied by many authors, see e.g., [1,[3][4][5][6][7], and so on. Many results about ruin probability have been obtained by above-mentioned references.…”

Section: Introductionmentioning

confidence: 99%