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Optimal Investment and Bounded Ruin Probability: Constant Portfolio Strategies and Mean-variance Analysis 1

Published online by Cambridge University Press:  17 April 2015

Ralf Korn  and
Anke Wiese
Ralf Korn
Affiliation:
Department of Methametics, University of Kaiserslautern and Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, 67653 Kaiserslautern, Germany, E-Mail: Korn@mathematik.uni-kl.de
Anke Wiese
Affiliation:
School of Mathematical and Computer Sciences and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, United Kingdom, E-Mail: A.Wiese@ma.hw.ac.uk
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Abstract

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We study the continuous-time portfolio optimization problem of an insurer. The wealth of the insurer is given by a classical risk process plus gains from trading in a risky asset, modelled by a geometric Brownian motion. The insurer is not only interested in maximizing the expected utility of wealth but is also concerned about the ruin probability. We thus investigate the problem of optimizing the expected utility for a bounded ruin probability. The corresponding optimal strategy in various special classes of possible investment strategies will be calculated. For means of comparison we also calculate the related mean-variance optimal strategies.

Keywords

Ruin ProcessOptimal InvestmentUtility Maximization under Constraints
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 2 , November 2008 , pp. 423 - 440
Copyright
Copyright © ASTIN Bulletin 2008

Footnotes

1

AMS 2000 subject classifications. 60G35, 90A09, 90A43.

References

Basak, S. and Shapiro, A. (2001) Value-at-risk-based risk management: optimal policies and asset prices. The Review of Financial Studies 14, 371–405.CrossRefGoogle Scholar
Browne, S. (1995) 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.CrossRefGoogle Scholar
Emmer, S. and Klüppelberg, C. (2004) Optimal portfolios when stock prices follow an exponential Lévy process. Finance and Stochastics 8, 17–44.CrossRefGoogle Scholar
Emmer, S., Klüppelberg, C. and Korn, R. (2001) Optimal portfolios with bounded capital at risk. Mathematical Finance 11, 365–384.CrossRefGoogle Scholar
Ferson, W.E. and Schadt, R.W. (1996) Measuring fund strategy and performance in changing economic conditions. The Journal of Finance 51, 425–461.CrossRefGoogle Scholar
Gandy, R. (2005) Portfolio optimization with risk constraints. PhD dissertation, University of Ulm.Google Scholar
Gaier, J., Grandits, P. and Schachermayer, W. (2003) Asymptotic ruin probabilities and optimal investment. Annals of Applied Probability 13, 1054–1076.CrossRefGoogle Scholar
Hipp, C. and Plum, M. (2000) Optimal investment for insurers. Insurance: Mathematics and Economics 27, 215–228.Google Scholar
Hipp, C. and Plum, M. (2003) Optimal investment for investors with state-dependent income, and for insurers. Finance and Stochastics 7, 299–321.CrossRefGoogle Scholar
Korn, R. and Korn, E. (2001) Option pricing and portfolio optimization: modern methods of financial mathematics. American Mathematical Society.Google Scholar
Loviscek, A.L. and Jordan, W.J. (2000) Stock selection based on Morningstar’s ten-year, five-star general equity mutual funds. Financial Services Review 9, 145–157.CrossRefGoogle Scholar
Merton, R.C. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373–413.CrossRefGoogle Scholar
Ng, K.W., Yang, H. and Zhang, L. (2004) Ruin probability under compound Poisson models with random discount factor. Probability in the Engineering and Informational Sciences 18, 55–70.CrossRefGoogle Scholar
Paulsen, J. (1998) Ruin theory with compounding assets – a survey. Insurance: Mathematics and Economics 22, 3–16.Google Scholar
Paulsen, J. (2002) On Cramér-like asymptotics for risk processes with stochastic return on investments. Annals of Applied Probability 12, 1247–1260.CrossRefGoogle Scholar
Perold, A.F., Sharpe, W.F. (1988) Dynamic Strategies for Asset Allocation. Financial Analysts Journal Jan/Feb, 16–27.CrossRefGoogle Scholar
Schmidli, H. (2005) On optimal investment and subexponential claims. Insurance: Mathematics and Economics 36, 25–35.Google Scholar
Yuen, K.C., Wang, G. and Ng, K.W. (2004) Ruin probabilities for a risk process with stochastic return on investments. Stochastic Processes and their Applications 110, 259–274.CrossRefGoogle Scholar