We design an incentive mechanism based on all-pay auctions for participatory sensing. The organizer (principal) aims to attract a high amount of contribution from participating users (agents) while at the same time lowering his payout, which we formulate as a profit-maximization problem. We use a contribution-dependent prize function in an environment that is specifically tailored to participatory sensing, namely incomplete information (with information asymmetry), risk-averse agents, and stochastic population. We derive the optimal prize function that induces the maximum profit for the principal, while satisfying strict individual rationality (i.e., strictly have incentive to participate at equilibrium) for both risk-neutral and weakly risk-averse agents. The thus induced profit is demonstrated to be higher than the maximum profit induced by constant (yet optimized) prize. We also show that our results are readily extensible to cases of risk-neutral agents and deterministic populations.