Once a debtor files for bankruptcy under Chapter 7, all or some of the unsecured debts are discharged and the debtor is endowed with a financial fresh start. However, a post-bankruptcy consumer faces restrictions on borrowing against future income and is likely to be liquidity constrained. This paper intends to provide a quantitative analysis regarding the effects of limits for borrowing against future income imposed on a post-bankruptcy consumer. We obtain explicit expressions for the optimal consumption, investment in the risky asset, and discretionary bankruptcy decision through a duality approach when there exists a liquidity constraint after bankruptcy. The quantitative results show that a post-bankruptcy constraint has significant impacts on a debtor’s consumption, investment, and bankruptcy wealth level. The effects of an opportunity to file for bankruptcy compete with those of post-bankruptcy liquidity constraints. We find the criterion for the latter to dominate the former. We also provide implications on the expected time to bankruptcy.

This paper investigates a continuous-time optimal consumption, investment, and life insurance decision problem of a family under inflation risk. In the financial market, there is a liquid inflation-linked index bond market which can be utilized to hedge the inflation risk. The explicit solutions are derived for constant relative risk aversion (CRRA) utility case by using martingale approach. The roles of index bond are investigated and it is verified that the index bond may have different roles depending on the market parameters. We analyze the effects of parameters on the optimal strategies with focus on the optimal demand for index bond and the optimal life insurance premium. Especially, the changes of expected inflation rate and volatility of inflation rate can have both positive and negative impacts on the life insurance premium and their quantitative impacts are considerable.