On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions

Bright Okore Osu; Silas Abahia Ihedioha; Joy Ijeoma Adindu-Dick

doi:doi:10.11648/j.ajam.20140201.12

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On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions

Bright Okore Osu, Silas Abahia Ihedioha, Joy Ijeoma Adindu-Dick

Published in American Journal of Applied Mathematics (Volume 2, Issue 1)

Received: 19 January 2014 Published: 20 February 2014

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Abstract

In this paper, the survival of insurance company’s investment with consumption is investigated under power and exponential utility functions. We take the risk reserve of an insurance company to follow Brownian motion with drift and tackle an optimal portfolio selection problem of the company. The investment case considered was insurance company that trades two assets: the money market account (bond) growing at a linear rate r and a risky stock with an investment behavior in the presence of a stochastic cash flow or a risk process, continuously in the economy.Under these functions, we obtained the optimal strategies. It is discovered that both utility functions are alike.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 1)
DOI	10.11648/j.ajam.20140201.12
Page(s)	8-13
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Stochastic Optimal Control, Company’s Investment With Consumption, Power Utility Function, Exponential Utility Function

References

[1]	Azcue,P.,Muler,N., (2009). Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints. Insurance: Mathematics and Economics. Volume 44, issue 1, 26-34.
[2]	Bai,L., Liu, J., (2007). Minimizing the probability of ruin under the interest force. Applied Mathematical Sciences. Volume 2, number 17, 843-851.
[3]	Bayraktar, E. Young, R. V., (2008). Minimizing the probability of ruin when the consumption is ratcheted. North American actuarial journal. Volume 12, number 4, 428-442.K. Elissa, "Title of paper if known," unpublished.
[4]	Browne, S., (1995). Optimal investment policies for a form with random risk process: exponential utility and minimizing the probability of ruin. Mathematics of operations research. 20,937-958.
[5]	Gaier, J., Grandits,P., (2002). Ruin probabilities in the presence of regularly varying tails and optimal investment. Insurance: Mathematics and Economics.Vol.30 Issue 2,211-217.
[6]	Iglehart, D. G., (1969). Diffusion Approximation in Collective Risk Theory. Journal of Applied Probability. 6, 285-292.
[7]	Kostadinova,R., (2007). Optimal investment for insurers, when the stock price follows an exponential Levy process. Insurance: Mathematics and Economics. Volume 41, Issue 2, 250-263.
[8]	Oksendal, B. Sulem, A., (2002). "Optimal consumption and portfolio with both fixed and proportional transaction costs." SIAM Journal on control and optimization. 40, 1765-1790.
[9]	Osu, B.O. and Ihedioha, S.A.,(2012)." Optimal Portfolio Selection for Pension Funds with Variable Rate of Return and Transaction Costs: Finite Horizon Case", Global Journal of Pure and Applied Mathematics, Volume 8, Number 3,275-286.
[10]	Osu, B.O. and Ihedioha, S.A.,(2013).Optimizing the returns and Probability of Survival of Insurance Company with time varying Investment returns. Journal of Advances in Mathematics vol. 3 no1, 152-158.
[11]	Osu, B.O. and Ihedioha, S.A.,(2013).Optimization of Time Varying Investment Returns of Insurance Company under Power Utility Function. International Journal of Statistika and Mathematika, ISSN: 2277- 2790 E-ISSN: 2249-8605, Volume 8, Issue 1, 2013 pp 42-50.
[12]	Wokiyi,D. (2012).Maximizing investment returns of an Insurance company while minimizing the probability of ruin. An M Sc thesis, University of Dar-es-Salam.

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APA Style

Bright Okore Osu, Silas Abahia Ihedioha, Joy Ijeoma Adindu-Dick. (2014). On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions. American Journal of Applied Mathematics, 2(1), 8-13. https://doi.org/10.11648/j.ajam.20140201.12

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ACS Style

Bright Okore Osu; Silas Abahia Ihedioha; Joy Ijeoma Adindu-Dick. On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions. Am. J. Appl. Math. 2014, 2(1), 8-13. doi: 10.11648/j.ajam.20140201.12

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AMA Style

Bright Okore Osu, Silas Abahia Ihedioha, Joy Ijeoma Adindu-Dick. On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions. Am J Appl Math. 2014;2(1):8-13. doi: 10.11648/j.ajam.20140201.12

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@article{10.11648/j.ajam.20140201.12,
  author = {Bright Okore Osu and Silas Abahia Ihedioha and Joy Ijeoma Adindu-Dick},
  title = {On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {8-13},
  doi = {10.11648/j.ajam.20140201.12},
  url = {https://doi.org/10.11648/j.ajam.20140201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140201.12},
  abstract = {In this paper, the survival of insurance company’s investment with consumption is investigated under power and exponential utility functions. We take the risk reserve of an insurance company to follow Brownian motion with drift and tackle an optimal portfolio selection problem of the company. The investment case considered was insurance company that trades two assets: the money market account (bond) growing at a linear rate r and a risky stock with an investment behavior in the presence of a stochastic cash flow or a risk process, continuously in the economy.Under these functions, we obtained the optimal strategies. It is discovered that both utility functions are alike.},
 year = {2014}
}

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TY  - JOUR
T1  - On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions
AU  - Bright Okore Osu
AU  - Silas Abahia Ihedioha
AU  - Joy Ijeoma Adindu-Dick
Y1  - 2014/02/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140201.12
DO  - 10.11648/j.ajam.20140201.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 8
EP  - 13
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ajam.20140201.12
AB  - In this paper, the survival of insurance company’s investment with consumption is investigated under power and exponential utility functions. We take the risk reserve of an insurance company to follow Brownian motion with drift and tackle an optimal portfolio selection problem of the company. The investment case considered was insurance company that trades two assets: the money market account (bond) growing at a linear rate r and a risky stock with an investment behavior in the presence of a stochastic cash flow or a risk process, continuously in the economy.Under these functions, we obtained the optimal strategies. It is discovered that both utility functions are alike.
VL  - 2
IS  - 1
ER  -

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Author Information

Bright Okore Osu

Department of Mathematics, Abia State University, Uturu, Nigeria
Silas Abahia Ihedioha

Government Secondary School Bwari Federal Capital Territory, Abuja, Nigeria
Joy Ijeoma Adindu-Dick

Department of Mathematics, Imo State University, Owerri, Nigeria

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APA Style

Bright Okore Osu, Silas Abahia Ihedioha, Joy Ijeoma Adindu-Dick. (2014). On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions. American Journal of Applied Mathematics, 2(1), 8-13. https://doi.org/10.11648/j.ajam.20140201.12

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ACS Style

Bright Okore Osu; Silas Abahia Ihedioha; Joy Ijeoma Adindu-Dick. On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions. Am. J. Appl. Math. 2014, 2(1), 8-13. doi: 10.11648/j.ajam.20140201.12

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AMA Style

Bright Okore Osu, Silas Abahia Ihedioha, Joy Ijeoma Adindu-Dick. On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions. Am J Appl Math. 2014;2(1):8-13. doi: 10.11648/j.ajam.20140201.12

Copy | Download

@article{10.11648/j.ajam.20140201.12,
  author = {Bright Okore Osu and Silas Abahia Ihedioha and Joy Ijeoma Adindu-Dick},
  title = {On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {1},
  pages = {8-13},
  doi = {10.11648/j.ajam.20140201.12},
  url = {https://doi.org/10.11648/j.ajam.20140201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140201.12},
  abstract = {In this paper, the survival of insurance company’s investment with consumption is investigated under power and exponential utility functions. We take the risk reserve of an insurance company to follow Brownian motion with drift and tackle an optimal portfolio selection problem of the company. The investment case considered was insurance company that trades two assets: the money market account (bond) growing at a linear rate r and a risky stock with an investment behavior in the presence of a stochastic cash flow or a risk process, continuously in the economy.Under these functions, we obtained the optimal strategies. It is discovered that both utility functions are alike.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - On the Survival of Insurance Company’s Investment with Consumption under Power and Exponential Utility Functions
AU  - Bright Okore Osu
AU  - Silas Abahia Ihedioha
AU  - Joy Ijeoma Adindu-Dick
Y1  - 2014/02/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140201.12
DO  - 10.11648/j.ajam.20140201.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 8
EP  - 13
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140201.12
AB  - In this paper, the survival of insurance company’s investment with consumption is investigated under power and exponential utility functions. We take the risk reserve of an insurance company to follow Brownian motion with drift and tackle an optimal portfolio selection problem of the company. The investment case considered was insurance company that trades two assets: the money market account (bond) growing at a linear rate r and a risky stock with an investment behavior in the presence of a stochastic cash flow or a risk process, continuously in the economy.Under these functions, we obtained the optimal strategies. It is discovered that both utility functions are alike.
VL  - 2
IS  - 1
ER  -

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