Optimal dividend and capital structure with debt covenants

Abstract : We consider an optimal dividend and capital structure problem for a firm which holds a certain amount of debt to which is associated a financial-ratio covenant between the creditors and the firm. We study optimal policies under a bankruptcy framework using a mixed reduced and structural approach in modelling default and liquidation times. Once in default, the firm is given a grace period during which it may inject more capital to correct the situation. The firm is liquidated if, by the end of the grace period, assets do not exceed the debt. Under this setup, we maximize the discounted amount of dividends distributed minus the capital injected up to the time of bankruptcy. It gives rise to a two-dimensional singular control problem leading to a non-standard system of variational inequalities. Beyond the usual viscosity characterization, we completely solve this problem and obtain a description of the continuation, dividend and capital injection regions enabling us to fully characterize the optimal policies. We conclude the paper with numerical results and illustrations.
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Submitted on : Tuesday, April 2, 2019 - 10:53:26 PM
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Etienne Chevalier, Vathana Ly Vath, Alexandre Roch. Optimal dividend and capital structure with debt covenants. 2019. ⟨hal-02088496⟩

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