This article investigates a stochastic control model for a pension fund which provides a variable death benefit to its members during the post-retirement period. The main framework model is described by two correlated fractional Brownian motions which correspond to investment and mortality risks, accordingly. Using the recent advanced results of stochastic control theory for fractional Brownian motion (fBm), we obtain the optimal Markovian control for the level of the death benefit. Finally, using a typical numerical example, we examine the effect of the Hurst exponent with respect to the different management decisions of the controlled variable.
- Carleman-type integral equation
- Fractional Brownian motion (fBm)
- Pension fund
- Stochastic linear quadratic optimal control