Optimal investment with transaction costs and dividends for an insurer
Bi, Junna1 ; Meng, Qingbin2
1 School of Statistics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, P.R. China.
2 Finance Department, School of Business, Renmin University of China, 59 Zhongguancun Street, Beijing 100872, P.R. China.
RAIRO - Operations Research - Recherche Opérationnelle, Special issue - Advanced Optimization Approaches and Modern OR-Applications, Tome 50 (2016) no. 4-5, pp. 845-855.

This paper investigates the optimal investment problems for an insurer whose reserve process is approximated by a diffusion model. The insurer is allowed to invest its wealth in the financial market consisting of one risk-free asset (bond) and one risky asset (stock). There are charges which equal to a fixed percentage of the amount transferred between the two assets. Under different criteria, we consider two optimization problems: one is maximizing the expected discounted utility of the dividends; the other is maximizing the insurer’s expected utility of the terminal wealth. We obtain that the optimal investment strategies are bang-bang strategies in both of the two problems. Numerical examples are given to illustrate our results.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016015
Classification : 91B28, 91B30
Mots-clés : Optimal investment, transaction costs, partial differential equation, dividend
Bi, Junna 1 ; Meng, Qingbin 2

1 School of Statistics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, P.R. China.
2 Finance Department, School of Business, Renmin University of China, 59 Zhongguancun Street, Beijing 100872, P.R. China. 
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Bi, Junna; Meng, Qingbin. Optimal investment with transaction costs and dividends for an insurer. RAIRO - Operations Research - Recherche Opérationnelle, Special issue - Advanced Optimization Approaches and Modern OR-Applications, Tome 50 (2016) no. 4-5, pp. 845-855. doi : 10.1051/ro/2016015. http://archive.numdam.org/articles/10.1051/ro/2016015/

S. Browne, Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin. Math. Oper. Res. 20 (1995) 937–957. | DOI | MR | Zbl

G.M. Costantinides, Capital Market Equilibrium with Transaction Cost. J. Polit. Econ. 9 (1986) 842–862. | DOI

M.H.A. Davis and A.R. Norman, Portfolio Selection with Transaction Costs. Math. Oper. Res. 15 (1990) 676–713. | DOI | MR | Zbl

W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions. Springer-Verlag, Berlin, New York (1993). | MR | Zbl

J. Gaier, P. Grandits and W. Schachermayer, Asymptotic ruin probabilities and optimal investment. Ann. Appl. Pr. 13 (2003) 1054–1076. | MR | Zbl

J. Grandell, Aspects of risk theory. Springer-Verlag, New York (1991). | MR | Zbl

H. Guan and Z. Liang, Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs. Insur. Math. Econ. 54 (2014) 109–122. | DOI | MR | Zbl

L. He and Z. Liang, Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs. Insur. Math. Econ. 44 (2009) 88–94. | DOI | MR | Zbl

C. Hipp and M. Plum, Optimal investment for insurers, Insur. Math. Econ. 27 (2000) 215–228. | DOI | MR | Zbl

K. Janeček and S. Shreve, Asymptotic analysis for optimal investment and consumption with transaction costs. Finance. Stoch. 8 (2004) 181–206. | DOI | MR | Zbl

Z. Jin, H. Yang and G. Yin, Optimal debt ratio and dividend payment strategies with reinsurance. Insur. Math. Econ. 64 (2015) 351–363. | DOI | MR | Zbl

H. Liu, Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets. J. Finance 59 (2004) 289–338. | DOI

H. Liu and M. Loewenstein, Optimal Portfolio Selection with Transaction Costs and Finite Horizons. Rev. Fin. Stud. 15 (2002) 805–835. | DOI

M.J.P. Magill and G.M. Constantinides, Portfolio Selection with Transaction Costs. J. Econ. Theory 13 (1976) 245–263. | DOI | MR | Zbl

R.C. Merton, Optimum Consumption and Portfolio Rules in a Continuous-Time Model. J. Econ. Theory 3 (1971) 373–413. | DOI | MR | Zbl

S.E. Shreve and H.M. Soner, Optimal investment and consumption with transaction costs. Ann. Appl. Probab. 4 (1994) 609–692. | DOI | MR | Zbl

Z. Wang, Xia J. and L. Zhang, Optimal investment for an insurer: The martingale approach. Insur. Math. Econ. 40 (2007) 322–334. | DOI | MR | Zbl

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