Optimal Investment and Debt Management Strategies in the Presence of Inflation Risks for a DC Pension Scheme
Abstract
This paper derives the optimal debt ratio, portfolio strategies and consumption rate for a Pension Fund Administrator (PFA) in a defined contributory (DC) pension scheme. Four asset classes were considered which include riskless asset, inflation-linked bonds, stocks and housing. Five background risks which include inflation, stock, housing, income growth rate and salary risks are considered. The plan member contributes a proportion of his or her stochastic salary into the scheme. The PFA make further effort to borrow money to finance her investment to ensure maximum returns. The contribution of the plan member in addition to borrowed capital is invested in financial and non-financial (housing) assets. In this paper, the real wealth process of the PFA is considered. The problem is formulated as a bi-objective stochastic control problem. The resulting Hamilton-Jacobi-Bellman (HJB) equation was solved using dynamic programming approach for stochastic process. This paper aims at (i) maximize the total expected discounted utility of consumption and debt of the PFA in an infinite time horizon, (ii) determine the optimal debt ratio and optimal consumption plan of the PFA, (iii) determine the optimal investment strategies for a PFA who invest in an economy that is exposed to five background risks. Using dynamic programming approach, we derive the optimal debt ratio, optimal consumption plan, optimal investment in inflation-linked bonds, stocks and housing for a PFA that chooses the power utility function. We found that the optimal debt ratio depends directly on the optimal real wealth. We also found that the optimal investment in stocks, housing and inflation-linked bonds depend on inflation, stock, salary, housing and income growth rate risks. Numerical implementation of the models using empirical data are presented.
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