Sovereign Debt Contract and Optimal Consumption-Investment Strategies

We present a model in which a sovereign country optimally decides on its consumption and investment policies as well as on the optimal time to default. In the paper we allow the sovereign borrower to keep the fraction of its augmented wealth in so-called international reserves. We further assume that these reserves can be deposited at the risk-free rate. In this framework, we obtain analytical solutions for optimal consumption and investment rules, as well as formulas for optimal default boundary and the value of the risky loan. In the paper we assume that in the case of default the lender can impose economic and political sanctions against the borrower and also can seize an implicit collateral. We show that when the country is getting very close to its default wealth level, then its relative risk aversion decreases and the country increases its consumption rate and the risky investment fraction at the expense of available liquid reserves.