Constant elasticity of variance model for proportional reinsurance and investment strategies. (English) Zbl 1231.91193

Summary: The insurer is allowed to buy reinsurance and invest in a risk-free asset and a risky asset. The claim process is assumed to follow a Brownian motion with drift, while the price process of the risky asset is described by the constant elasticity of variance (CEV) model. The Hamilton-Jacobi-Bellman (HJB) equation associated with the optimal reinsurance and investment strategies is established, and solutions are found for insurers with CRRA or CARRA utility.


91B30 Risk theory, insurance (MSC2010)
49L20 Dynamic programming in optimal control and differential games
Full Text: DOI


[1] Cai, J.; Tan, K. S.; Weng, C.; Zhang, Y., Optimal reinsurance under VaR and CTE risk measures, Insurance: Mathematics and Economics, 43, 185-196 (2008) · Zbl 1140.91417
[2] Cao, Y.; Wan, N., Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation, Insurance: Mathematics and Economics, 45, 157-162 (2009) · Zbl 1231.91150
[3] Cerqueti, R.; Foschi, R.; Spizzichino, F., A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts, Insurance: Mathematics and Economics, 45, 59-64 (2009) · Zbl 1231.91152
[4] Cox, J. C., The constant elasticity of variance option pricing model, The Journal of Portfolio Management, 22, 16-17 (1996)
[5] Davydov, D.; Linetsky, V., The valuation and hedging of barrier and lookback option under the CEV process, Management Science, 47, 949-965 (2001) · Zbl 1232.91659
[6] Detemple, J.; Tian, W. D., The valuation of American options for a class of diffusion processes, Management Science, 48, 917-937 (2002) · Zbl 1232.91660
[7] Devolder, P.; Bosch, P. M.; Dominguez, F. I., Stochastic optimal control of annuity contracts, Insurance: Mathematics and Economics, 33, 227-238 (2003) · Zbl 1103.91346
[8] Gao, J., Optimal portfolios for DC pension plans under a CEV model, Insurance: Mathematics and Economics, 44, 479-490 (2009) · Zbl 1162.91411
[9] Heston, S., A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, 6, 327-343 (1993) · Zbl 1384.35131
[10] Hipp, C.; Vogt, M., Optimal dynamic XL reinsurance, ASTIN Bulletin, 33, 193-207 (2003) · Zbl 1059.93135
[11] Jones, C., The dynamics of the stochastic volatility: evidence from underlying and options markets, Journal of Econometrics, 116, 181-224 (2003) · Zbl 1016.62122
[12] Lo, C. F.; Yuen, P. H.; Hui, C. H., Constant elasticity of variance option pricing model with time-dependent parameters, International Journal of Theoretical and Applied Finance, 3, 661-674 (2000) · Zbl 1006.91050
[13] Promislow, D. S.; Young, V. R., Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Juounal, 9, 109-128 (2005) · Zbl 1141.91543
[14] Taksar, M.; Markussen, C., Optimal dynamic reinsurance policies for large insurance portfolios, Finance and Stochastics, 7, 97-121 (2003) · Zbl 1066.91052
[15] Widdicks, M.; Duck, P.; Andricopoulos, A.; Newton, P., The Black-Scholes equation revisited: symptotic expansions and singular perturbations, Mathematical Finance, 15, 373-391 (2005) · Zbl 1124.91342
[16] Xiao, J.; Zhai, H.; Qin, C., The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts, Insurance: Mathematics & Economics, 40, 302-310 (2007) · Zbl 1141.91473
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.