Partial Equilibrium And Market Completion

We consider financial markets with agents exposed to an external source of risk which cannot be hedged through investments on the capital market alone. The sources of risk we think of may be weather and climate. Therefore we face a typical example of an incomplete financial market. We design a model of a market on which the external risk becomes tradable. In a first step we complete the market by introducing an extra security which valuates the external risk through a process parameter describing its market price. If this parameter is fixed, risk has a price and every agent can maximize the expected exponential utility with individual risk aversion obtained from his risk exposure on the one hand and his investment into the financial market consisting of an exogenous set of stocks and the insurance asset on the other hand. In the second step, the market price of risk parameter has to be determined by a partial equilibrium condition which just expresses the fact that in equilibrium the market is cleared of the second security. This choice of market price of risk is performed in the framework of nonlinear backwards stochastic differential equations.