International Journal of Advances in Mathematics
International Journal of Advances in Mathematics
2456-6098
Volume 2017
Number 6
2017
November
01
Portfolio Strategy for an Investor with Stochastic Premium Under Exponential Utility via Legendre Transform and Dual Theory
27
35
EN
Edikan
E
Akpanibah
Department of Mathematics and Statistics, Federal University Otuoke, P.M.B 126, Yenagoa, Bayelsa State,
Nigeria.
Bright
O. Osu
Department of Mathematics, Michael Okpara University of Agriculture, Umudike Abia State, Nigeria.
osu.bright@mouau.edu.ng
We investigate the optimal investment strategies of an insurance company. We assume that the rates at which premiums are paid to insurance companies are stochastic, the total claims are modeled by a compound Poisson process, we assume that surplus of the insurance company is invested in risk free asset and in a risky asset such as stocks. We applied the Jacobi Hamilton-Jacobi-Bellman equation to obtain an optimized problem and used the Legendre transform and dual theory to obtain the optimal investment strategy for constant absolute risk aversion (CARA) utility function. Our result will enables insurance companies to determine the proportion of their wealth to be invested in risk-free asset and a risky asset in order to optimize profit knowing full well it has responsibility to pay the policy holders whenever there is claims occurrence.
Investment Strategy, Stochastic Premium ,Under Exponential Utility, Legendre Transform and Dual Theory.
http://adv-math.com/2017/11/01/edikan-e-akpanibah-bright-o-osu-portfolio-strategy-investor-stochastic-premium-exponential-utility-via-legendre-transform-dual-theory-volume-2017-number-6-pages-27-35/
http://adv-math.com/wp-content/uploads/2017/10/ADV-201734.pdf