Geodesic
Optimal investment strategy for a non-life insurance company: quadratic loss
/Lukasz Delong1
1 Division of Probabilistic Methods Institute of Econometrics Warsaw School of Economics Al. Niepodleg/lo/sci 162 02-554 Warszawa, Poland
Applicationes Mathematicae, Tome 32 (2005) no. 3, pp. 263-277 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The aim of this paper is to construct an optimal investment strategy for a non-life insurance business. We consider an insurance company which provides, in exchange for a single premium, full coverage to a portfolio of risks which generates losses according to a compound Poisson process. The insurer invests the premium and trades continuously on the financial market which consists of one risk-free asset and $n$ risky assets (Black–Scholes market). We deal with the insurer's wealth path dependent disutility optimization problem and apply a quadratic loss function which penalizes deviations below a reserve for outstanding liabilities as well as above a given upper barrier. An optimal investment strategy is derived using stochastic control theory in the absence of constraints on control variables. Some properties of the strategy and the behaviour of the insurer's wealth under the optimal control are investigated. The set up of our model is more general, as it can also be used in non-life loss reserving problems.
DOI : 10.4064/am32-3-2
Keywords: paper construct optimal investment strategy non life insurance business consider insurance company which provides exchange single premium full coverage portfolio risks which generates losses according compound poisson process insurer invests premium trades continuously financial market which consists risk free asset risky assets black scholes market insurers wealth path dependent disutility optimization problem apply quadratic loss function which penalizes deviations below reserve outstanding liabilities above given upper barrier optimal investment strategy derived using stochastic control theory absence constraints control variables properties strategy behaviour insurers wealth under optimal control investigated set model general non life loss reserving problems

/Lukasz Delong 1

1 Division of Probabilistic Methods Institute of Econometrics Warsaw School of Economics Al. Niepodleg/lo/sci 162 02-554 Warszawa, Poland 
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/Lukasz Delong. Optimal investment strategy for a non-life
 insurance company: quadratic loss. Applicationes Mathematicae, Tome 32 (2005) no. 3, pp. 263-277. doi: 10.4064/am32-3-2

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