Defined Contribution Pension Planning with the Return of Premiums Clauses and HARA Preference in Stochastic Environments

This paper studies a defined contribution(DC)pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment.In practice,most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement.In the mathematical modeling,we assume that a part of pension members could withdraw their premiums if they died before retirement and surviving members could equally share the difference between accumulated contributions and returned premiums.We suppose that the financial market consists of a risk-free asset,a stock,and a zero-coupon bond.The interest rate is driven by a stochastic affine interest rate model and the stock price follows the Heston’s stochastic volatility model with stochastic interest rates.Different fund managers have different risk preferences,and the hyperbolic absolute risk aversion(HARA)utility function is a general one including a power utility,an exponential utility,and a logarithm utility as special cases.We are concerned with an optimal portfolio to maximize the expected utility of terminal wealth by choosing the HARA utility function in the analysis.By using the principle of dynamic programming and Legendre transform-dual theory,we obtain explicit solutions of optimal strategies.Some special cases are also derived in detail.Finally,a numerical simulation is provided to illustrate our results.

Optimal Consumption and Portfolio Decision with Heston's SV Model Under HARA Utility Criterion

This paper studies the optimal consumption-investment strategy with Heston’s stochastic volatility(SV) model under hyperbolic absolute risk aversion(HARA) utility criterion. The financial market is composed of a risk-less asset and a risky asset, whose price process is supposed to be driven by Heston’s SV model. The risky preference of the individual is assumed to satisfy HARA utility,which recovers power utility, exponential utility and logarithm utility as special cases. HARA utility is of general framework in the utility theory and is seldom studied in the existing literatures. Legendre transform-dual technique along with stochastic dynamic programming principle is presented to deal with our problem and the closed-form solution to the optimal consumption-investment strategy is successfully obtained. Finally, some special cases are derived in detail.