Abstract

Retirees meet a number of problems as they are growing older which needs persistent attention. Therefore, the decisions of the people who are close to retirement are affected undoubtedly by the consequences of financial markets. In the proposed model, stock price dynamics is assumed to follow Geometric Brownian motion (GBM) and our goal was to maximize the expected discounted utility of consumption and terminal wealth with health expenses. The investment return process comprises risk free asset and risky assets, and the health expenses. We choose power utility functions where comprehensive solutions for Hyperbolic Absolute Risk Aversion (HARA) utility functions are obtained and optimal in vestment, consumption and health expenditure strategies are derived by applying dynamic programming and variable change technique on the Hamilton-Jacobi-Bellman (HJB) equations. The inflation price market risk governs the amount invested in stock, bond and also how much to be put in health to sustain a given period of the retiree’s lifetime. We also investigated the effects of correlation coefficients. When the value of the constant variance discounting coefficient becomes larger experienced enterprise annuity retiree reduce the proportion of their investment in the risky asset. As the health welfare rate R increases, the proportion of wealth invested in the stock becomes larger. We found that when the rate of investing in health is too high, injecting too much capital into the risky assets causes greater economic loss to the retiree’s interest. Finally, a numerical example is presented to characterize the impacts of financial parameters on the optimal investment consumption strategy with health expenditure.

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School	: School of Natural and Applied Sciences
Issued Date	: 2023

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