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We study the problem of pricing variable annuities with a multi-layer expensestrategy, under which the insurer charges fees from the policyholder's accountonly when the account value lies in some pre-specified disjoint intervals,where on each pre-specified interval, the fee rate is fixed and can bedifferent from that on other interval. We model the asset that is theunderlying fund of the variable annuity by a hyper-exponential jump diffusionprocess. Theoretically, for a jump diffusion process with hyper-exponentialjumps and three-valued drift, we obtain expressions for the Laplace transformsof its distribution and its occupation times, i.e., the time that it spendsbelow or above a pre-specified level. With these results, we derive closed-formformulas to determine the fair fee rate. Moreover, the total fees that will becollected by the insurer and the total time of deducting fees are alsocomputed. In addition, some numerical examples are presented to illustrate ourresults.

Pricing variable annuities with multi-layer expense strategy