Optimal investment for an insurer in the Lévy market: the martingale approach. (English) Zbl 1169.91380

Summary: We apply the martingale approach, which has been widely used in mathematical finance, to study the optimal investment problem for an insurer. When the risk and security assets are described by the Lévy processes and utility is CARA, the closed-form solutions to the maximization problem are obtained.


91B28 Finance etc. (MSC2000)
60G44 Martingales with continuous parameter
Full Text: DOI


[1] Browne, S., Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin, Mathematics of Operations Research, 20, 937-958 (1995) · Zbl 0846.90012
[2] Cont, R.; Tankov, P., (Financial Modelling With Jump Processes. Financial Modelling With Jump Processes, Chapman and Hall/CRC Financial Mathematics Series (2003)) · Zbl 1052.91043
[3] Hipp, C.; Plum, M., Optimal investment for insurers, Insurance: Mathematics and Economics, 27, 215-228 (2000) · Zbl 1007.91025
[4] Hipp, C., Stochastic control with application in insurance, (Stochastic Methods in Finance. Stochastic Methods in Finance, Lecture Notes in Mathematics, vol. 1856 (2004), Springer: Springer Berlin), 127-164 · Zbl 1134.91024
[5] Karatzas, I.; Lehoczky, J. P.; Shreve, S. E.; Xu, G. L., Martingale and duality methods for utility maximization in incomplete markets, SIAM Journal on Control and Optimization, 29, 702-730 (1991) · Zbl 0733.93085
[6] Kramkov, D.; Schachermayer, W., The asymptotic elasticity of utility functions and optimal investment in incomplete markets, Annals of Applied Probability, 9, 904-950 (1999) · Zbl 0967.91017
[7] Liu, C. S.; Yang, H., Optimal investment for an insurer to minimize its probability of ruin, North American Actuarial Journal, 8, 11-31 (2004) · Zbl 1085.60511
[8] Yang, H.; Zhang, L., Optimal investment for insurer with jump-diffusion risk process, Insurance: Mathematics and Economics, 37, 615-634 (2005) · Zbl 1129.91020
[9] Wang, N., Optimal investment for an insurer with exponential utility preference, Insurance: Mathematics and Economics, 40, 77-84 (2007) · Zbl 1273.91431
[10] Wang, Z.; Xia, J.; Zhang, L., Optimal investment for an insurer: The martingale approach, Insurance: Mathematics and Economics, 40, 322-334 (2007) · Zbl 1141.91470
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.