Pension funding problem with regime-switching geometric Brownian motion assets and liabilities

This paper extends the pension funding model in (N. Am. Actuarial J. 2003; 7:37–51) to a regimeswitching case. The market mode is modeled by a continuous-time stationary Markov chain. The asset
value process and liability value process are modeled by Markov-modulated geometric Brownian motions.
We consider a pension funding plan in which the asset value is to be within a band that is proportional
to the liability value. The pension plan sponsor is asked to provide sufficient funds to guarantee the asset
value stays above the lower barrier of the band. The amount by which the asset value exceeds the upper
barrier will be paid back to the sponsor. By applying differential equation approach, this paper calculates
the expected present value of the payments to be made by the sponsor as well as that of the refunds to the
sponsor. In addition, we study the effects of different barriers and regime switching on the results using
some numerical examples. The optimal dividend problem is studied in our examples as an application of
our theory.