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Application of Generalized Geometric Itô-Lévy Process to Investment-Consumption-Insurance Optimization Problem under Inflation Risk
Botswana International University of Science and Technology, Palapye, Botswana
- 1 Botswana International University of Science and Technology, Palapye, Botswana
Journal of Mathematical Finance·Volume 11 (2021)·Pages 163–175·Published 1 March 2021·DOI10.4236/jmf.2021.112008
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Abstract
We consider a problem of maximizing the utility of an agent who invests in a stock, money market account and an index bond incorporating life insurance, deterministic income, and consumption. The stock is assumed to be a generalized geometric It?-Lévy process. Assuming a power utility function, we determine the optimal investment-consumption-insurance strategy under inflation risk for the investor in a jump-diffusion setting using martingale approach.
KeywordsUtility TheoryPortfolio OptimizationStochastic ControlItô-Lévy DiffusionsMartingale MethodLife Insurance
- Markowitz, H. (1952) Portfolio Selection. Journal of Finance, 7, 77-91. https://doi.org/10.2307/2975974
- Merton, R.C. (1971) Optimum Consumption and Portfolio Rules in a Continuous-Time Case. Journal of Economic Theory, 3, 373-413.
- Merton, R.C. (1969) Lifetime Portfolio Selection under Uncertainty: The Continuous Time Model. Review of Economics and Statistics, 51, 247-257. https://doi.org/10.2307/1926560
- Zhang, B., Peng, J. and Shengguo, L. (2015) Uncertian Programming Models for Portfolio Selection with Uncertain Returns. International Journal of Systems Science, 46, 2510-2519. https://doi.org/10.1080/00207721.2013.871366
- Chen, L., Peng, J., Zhang, B. and Rosyida, I. (2017) Diversified Models for Portfolio Selection on Uncertain Semivariance. International Journal of Systems Science, 48, 637-648. https://doi.org/10.1080/00207721.2016.1206985
- Huang, H., Milevsky, M.A. and Wang, J. (2008) Portfolio Choice and Life Insurance: The CRRA Case. Journal of Risk and Insurance, 75, 847-872. https://www.jstor.org/stable/25145313
- Kraft, H. and Steffensen, M. (2008) Optimal Consumption and Insurance: A Continuous-Time Markov Chain Approach. ASTIN Bulletin, 28, 231-257.
- Guambe, C. and Kufakunesu, R. (2015) A Note on Optimal Investment-Consumption-Insurance in a Levy Market. Journal of Insurance: Matheathematics and Economics, 65, 30-36. https://doi.org/10.1016/j.insmatheco.2015.07.008
- Wang, H., Wang, R., Wei, J. and Xu, S. (2019) Optimal Investment-Consumption-Insurance Strategy in a Continuous-Time Self-Exciting Threshold Model. Journal of Communications in Statistics—Theory and Methods, 48, 3530-3548. https://doi.org/10.1080/03610926.2018.1477161
- Guambe, C. and Kufakunesu, R. (2020) Optimal Investment-Consumption and Life Insurance with Capital Constraints. Journal of Communications in Statistics—Theory and Methods, 49, 648-669. https://doi.org/10.1080/03610926.2018.1549246
- Kronborg, M.T. and Steffensen, M. (2015) Optimal Consumption, Investment and Insurance with Surrender Option Guarantee. Journal of Insurance: Mathematics and Economics, 48, 178-188. https://doi.org/10.1080/03461238.2013.775964
- Kronborg, M.T. (2014) Optimal Consumption and Investment with Labour Income and European/American Capital Garantee, Risks, MDPI. Open Access Journal, 2, 171-194. https://doi.org/10.3390/risks2020171
- Brennan, J.M. and Xia, Y. (2002) Dynamic Asset Allocation under Inflation. Journal of Finance, 57, 1201-1238. https://www.jstor.org/stable/2697777