This paper considers interdependent electric power and gas supply networks and investigates a dynamic contract mechanism between risk-averse prosumers and a risk-neutral aggregator. The aggregator tries to manage not only financial risks but also power energy and gas energy generated by the prosumers in the presence of uncertain and volatile risk of energy generation processes. The aggregator will determine an incentive condition required of the prosumers so as to indirectly control their actions preferable for the aggregator. We first formulate a novel dynamic contract problem, where each prosumer minimizes an exponential-type cost functional with risk aversion under energy dynamical systems. The problem is regarded as a principal-agent problem in contract theory and the prosumers' optimization problem can be reduced to a Linear Exponential Quadratic Gaussian dynamic game problem. Most part of the solution to the problem considered here can be obtained analytically, while we need to employ a numerical optimization technique to determine the aggregator's action. The effectiveness of the risk-sharing between aggregator and prosumers induced by the proposed mechanism is demonstrated through a simulation.