Optimal financial contracts with unobservable investments

In this article we propose a security-design problem in which risk neutral entrepreneurs make unobservable investment decisions while employing the investment funds of risk-neutral outside investor/creditor(s). Contracts are restricted to satisfy limited liability and monotonicity of the payment schedule. The model we present extends the classical one proposed by Innes (1990, Journal of Economic Theory 52, 47-67) along three main directions: agents' decisions may be restricted by their initial capital and outside financial opportunities; their investment decisions may also consist in hiding funds in an asset placed outside their firms; initial firms' capital, which identifies entrepreneur types, may only be imperfectly observed by creditors (i.e. types are private information). We motivate our interest in this security-design problem referring to the 'opacity' that often characterizes the financial situation and decisions of small firms, a particularly large fraction of the non-financial sector in most developed countries.